Who are you, exactly?

I suspect mine isn't the majority view but the banter->sex "pipeline" is a misnomer. The point is the banter! For the usual reasons of making friends, having fun, breaking ice, as you say in another comment. And then as a side effect, if there's sexual compatibility, I might realize that Im not just-attracted to this person but actually want to go be physically intimate with them. (As I know you know since you've written about it elsewhere: there's a big difference between attraction and the prediction that hooking up will be fun.)

Again this may be idiosyncratic but IMO thinking of it as a pipeline at all is a major thing that screws guys up and makes women (and men) frustrated. Banter in the sense of this post is not for seduction! (Verbal dirty-dancing does seem like a fine sex pipeline but doesn't seem like the "banter" thing.) So I see a bunch of inept guys activate the "let's have fun and be friends and break the ice" banter game with women (who accept the false invitation,) and then embarrass/frustrate everyone when they reveal one way or another that their primary (or sole) intent was sex.

Banter "works" in the sense that if you really get along with a person, you both might find it easy to imagine it being fun to have sex with each other, and mutually believing that probably makes actual seduction attempts go way better.

I find myself suddenly less sure that you don't/can't experience the same companionate love that I do, which may or may not be the same as everyone else. Being on a team in the way you describe here, with the expectations and predictions of what that means as you describe here, "those little moment to moment coordinations," etc, seems like a typical sample from the distribution of what I write when someone asks me to try to describe what the value proposition of relationships/love is. It reads to me like a pretty fair description of what I mean when I say (an idealized form of) "companionship."  I think my version might have included more retrospectively non-central accounts of specific forms of emotional support (which I think you've metaphorically quirked an eyebrow at in the past) but right now it seems like those are implementation details of this core thing. (E.x. I've said things like "a promise to be there for the other, to pick them up if they need or want the help, etc" but that's only actually a warm thought when underlying that dynamic is the belief that the two are a team in the way I interpret what you describe above.)

Might "uninhibited" or "unfiltered" be closer to the concept you're going for here?

(Written quickly, and therefore not compactly, in the shower. Apologies.)

I have suspected for a while that there is instrumental value in oxytocin/companionate-love/etc, beyond the terminal 'niceness' of it.

Consider alcohol (or other inhibition-lowering drugs): 

•  Bars are, apparently, the standard place to meet up after work and relax in lots of cultures
• Ensuring there is sufficient wine/alcohol at a dinner party (or parties of any sort) is IME considered a top priority
• At parties, it is a meme that high schoolers are taught to fight that folks (especially the host) will frequently at least lightly suggest that you have a drink/other similar drug

Intuitively to me, "~everyone will have a better time here / this way compared to the alternative." But why? I think a large part of it is that folks who have had alcohol before both know how it effects them (it makes them more likely to speak their mind and/or feel friendly toward others and/or take risks social or otherwise) and, the key part: they also believe it effects everyone else roughly the same way. If everyone at the party knows that everyone else is getting drunk, if there is common knowledge that everyone is lowering their guard, then everyone feels safe and relaxed enough to in fact lower theirs. Social frictions get smoothed and higher value social risks get taken (e.g. dancing, asking someone out, etc), 

I think oxytocin/companionate love plays a very similar role on the level of personal relationships (of all kinds.) If there is common knowledge that the individuals are drunk on love/connection (or at least buzzed,) then there is a commonly known joint belief that the other will seek to overlook flaws, establish greater trust, make good faith efforts toward the other's values, look out for the other in a general sense, .... And when that is believed by all participants, alliances on all levels (professional, friendly, romantic,...) are made much more frequently, easily, and held more strongly. 

This is a large part of why, I think, that there is often such delighted interest from others in whether one is drunk/drugged...and similarly why there is such delighted and/or profoundly serious interest in whether one feels love toward another. Having common knowledge about everyone under the same or similar influence is a majority of the value to be had.

Last piece of the model: Being drunk/drugged among people you don't already trust is, as I understand, commonly considered to be a Bad Time, and I think it's because you've made yourself more vulnerable but have no assurance that others are more likely to trust you in kind. I claim that it is for similar reasons that people become very impassioned about the question of "Does X really love me?" If one person is sipping on that oxytocin, and the other one isn't, then that creates a serious asymmetric vulnerability.

At least that's my model of a significant chunk of the instrumental value / import / function of oxytocin to human brains in particular.

So with all that established: Contrary to the post title: If you (John) find some way to temporarily shoot up with oxytocin that works, there may be human-relationship/coordination circumstances where you (John) might want to do so as an instrumental act toward satisfying non-companionate-love values.

Thanks for the check! I've added a collab containing my quick numerical stress tests, linked at the bottom of the post.

(Update 7)

After some back and forth last night with an LLM^[1], we now have a proof of "chainability" for the redundancy diagrams in particular. (And have some hope that this will be most of what we need to rescue the stochastic->deterministic nat lat proof.)

(Theorem) Chainability of Redunds

Let P be a distribution over $X_1$, $X_2$, and $\Lambda$.
Define:
$Q[X,\Lambda ]:=P\left[X\right]P\left[\Lambda |X_1\right]$
$S[X,\Lambda ]:=P\left[X\right]P\left[\Lambda |X_2\right]=P\left[X\right]{\sum }_{X_1}P\left[X_1|X_2\right]P\left[\Lambda |X\right]$$R[X,\Lambda ]:=P\left[X\right]Q\left[\Lambda |X_2\right]=P\left[X\right]{\sum }_{X_1}P\left[X_1|X_2\right]P\left[\Lambda |X_1\right]$

Where you can think of Q as 'forcing' P into factorizing per one redundancy pattern: $X_2\to X_1\to \Lambda$, S as forcing the other pattern: $X_1\to X_2\to \Lambda$, and R as forcing one after the other: first $X_2\to X_1\to \Lambda$, and then $X_1\to X_2\to \Lambda$.

The theorem states,
$D_{KL}\left(P||R\right)\le D_{KL}\left(P||Q\right)+D_{KL}\left(P||S\right)$, 

Or in words: The error (in $D_{KL}$ from $P$) accrued by applying both factorizations to P, is bounded by the the sum of the errors accrued by applying each of the factorizations to P, separately.

Proof

The proof proceeds in 3 steps.

1.  $D_{KL}\left(P||Q\right)\ge D_{KL}\left(S||R\right)$

   Pf.
   Let $a_{X_1}:=P\left[X_1|X_2\right]P\left[\Lambda |X\right]\ge 0$

   Let $b_{X_1}:=P\left[X_1|X_2\right]P\left[\Lambda |X_1\right]\ge 0$

   By the log-sum inequality:

   ${\sum }_{X_1}\left(a_{X_1}ln\frac{a_{X_1}}{b_{X_1}}\right)\ge \left({\sum }_{X_1}{a}_{X_1}\right)ln\left(\frac{{\sum }_{X_1}{a}_{X_1}}{{\sum }_{X_1}{b}_{X_1}}\right)$

   $⟹$$D_{KL}\left(P||Q\right)\ge D_{KL}\left(S||R\right)$ as desired.

2. $D_{KL}\left(P||R\right)=D_{KL}\left(P||S\right)+D_{KL}\left(S||R\right)$

   Pf.

   $D_{KL}\left(P||R\right)-D_{KL}\left(P||S\right)$

   $={\sum }_{X,\Lambda }P[X,\Lambda ]\left[lnP\right[\Lambda |X]-lnR[\Lambda |X_2]-lnP[\Lambda |X]+lnS[\Lambda |X_2\left]\right]$

   $={\sum }_{X_2}P\left[X_2\right]{\sum }_{\Lambda }{\sum }_{X_1}P\left[X_1|X_2\right]P\left[\Lambda |X\right]ln\frac{S\left[\Lambda |X_2\right]}{R\left[\Lambda |X_2\right]}$

   $={\sum }_{X_1}{\sum }_{X_2}P\left[X_1|X_2\right]P\left[X_2\right]{\sum }_{\Lambda }S\left[\Lambda |X_2\right]ln\frac{S\left[\Lambda |X_2\right]P\left[X\right]}{R\left[\Lambda |X_2\right]P\left[X\right]}$

   $=D_{KL}\left(S||R\right)$

3.  Combining steps 1 and 2,
   $D_{KL}\left(P||Q\right)\ge D_{KL}\left(S||R\right)=D_{KL}\left(P||R\right)-D_{KL}\left(P||S\right)$

   $⟹D_{KL}\left(P||R\right)\le D_{KL}\left(P||Q\right)+D_{KL}\left(P||S\right)$

   which completes the proof.

Notes:
In the second to last line of step 2, the expectation over $P\left[X_1|X_2\right]$ is allowed because there are no free $X_1$'s in the expression. Then, this aggregates into an expectation over $S[X,\Lambda ]$ as $S\left[\Lambda |X_2\right]=S\left[\Lambda |X\right]$.

We are hopeful that this, thought different than the invalidated result in the top level post, will be an important step to rescuing the stochastic natural latent => deterministic natural latent result.
 

1. ^{^}

   A (small) positive update for me on their usefulness to my workflow!

(Update 5)

A conjecture we are working on which we expect to be generally useful beyond possibly rescuing the stoch->det proof that used to rely on the work in this post:

Chainability (Conjecture):
$\forall P[X,\Lambda ]$with ${ϵ}_1:=D_{KL}(X_1\to X_2\to \Lambda )$, ${ϵ}_2:=D_{KL}(X_1\leftarrow \Lambda \to X_2)$,
Define  $Q[X,\Lambda ]:=P\left[X\right]P\left[\Lambda |X_2\right]$, and  $Q^{\prime }[X,\Lambda ]:=Q\left[X_1|\Lambda \right]Q\left[X_2|\Lambda \right]Q\left[\Lambda \right]$.
Then, $D_{KL}\left(P||Q\right)<n({ϵ}_1+{ϵ}_2)$

Here is a collab with a quick numerical test that suggests the bound holds (and that n=1, in this case).

(Note: The above as written is just one step of chaining, and ultimately we are hoping to show it holds for arbitrarily many steps, accumulating an associated number of epsilons as error.)

Do you have sympy code for the example noted at the bottom of the collab that claims a ratio of > 9.77 including the mediation $D_{KL}$? I tried with the parameters you mention and am getting a ratio of ~3.4 (which is still a violation of previous expectations, tbc.)

(Update 2)

Taking the limit of the ratio of $D_{KL}$s (using summation rather than max) with $c\to 0$ while $b:=10c$ gives $5\left(\frac{r+1}{11}\right)$

Setting c very small and ramping up r indeed brakes the bound more and more severely. (Code changes from the collab you provided, below.)