Hello! This sounds like a great extension of some existing tools (from various smartphone-based apps, to things like Pavlok) but with contemporary AI to enable a much wider range of applicable scenarios. As someone who has genuinely considered hiring someone to look over my shoulder all day, I wish you & your product success!
One thing I notice, however, is that the use-case appears to be limited to scenarios in which there is a determined target behavior to do or to not-do. My main struggle, in terms of literal 'control of my self & actions', is determining where to apply my time & energy. This would be true even if I were a single person renting an apartment, as I have numerous "projects" competing for time, but is considerably more difficult because I have a family and a house and debts, which (seemingly) add up to more demands than can be met simultaneously. Though here I may be conflating broader "executive functioning" with the more narrow "self-control".
Not addressing this is not a defect of your product, in any way. I make this comment only to suggest a more tempered language about the product, in part to ensure that your users come in with a similarly-tempered expectation.
My (three) children are still young, so my perspective is limited, but it seems to me that the main concerns about screen time stem less from the screen-as-medium, itself, and more from applying the same sets of concerns to the virtual/media environment that are applied to the physical world -- that is, concerns about unsupervised children encountering potentially serious harms.
Some parents may face constraints such that it could be judged reasonable to turn their kids loose with a screen in order to do whatever else needs to get done. People live in a wide variety of imaginable and unimaginable circumstances. For me though, and for other folks fortunate enough to not face such constraints, screen time just shouldn't be unsupervised -- it should be modeled as something to be actively engaged with, and appropriately limited.
When I turn on a show for my kids, I sit and watch it with them unless it's both known to be "safe", and I have something I need to attend to in that moment. I often paraphrase dialogue so they can understand what's going on and being said ("she means what the other person did wasn't polite", "that's how they used to say they need to use the bathroom", etc), or ask them questions about it ("do you think they really meant they were surprised, or that they only said they were in order to hide being afraid?", "how do you suppose they get the camera into the mole burrows like that, and without scaring the moles?", etc), and if I've chosen something with scenes that either have adult themes they don't need yet, or it's one of those cartoon movies that seemed contractually obligated to include a traumatic scene, I simply skip it in the moment, and if anything important to the plot happened in that section, I'll explain what it was. Just because it's there doesn't mean you have to sit and take it.
Honestly, the same is true for chapter-book bedtime stories.
And Cocomelon certainly has a presence, but averaging out to a rate of about one per day at its peak. It's a way to listen to songs sung by better voices than mine, though I almost always sing along, to show that singing is something to participate in, not just take in. It's also been a way to learn new songs, or song-motions, to then to together at other times or in the car. Some of the activities the too-smooth-looking kids get up to in the videos have also been taken as inspiration for things to do in real life: make "rainbow popsicles", make a box into a train and push it around, etc.
In that way, it flows pretty naturally with the other snippets of media they get with me: kid-safe sections from movies like Dune or Jurassic Park (for the visuals and for the bigger plot-themes about bravery, hubris, etc), videos of unique creations like Wintergatan's Marble Machine or Theo Jansen's Strandbeest, rocket launches, of course, and even slice-of-life videos like "Kids in Other Countries" (https://www.kiocs.org/).
I am reminded of this paper, on the equivalence of information-theoretic formalisms and those of physics. I am linking the paper here not as an endorsement, but because it may provide some unusual, but useful, lines of thought.
You mention both "local" and "cosmic" unfairness, but the body of the post appears to focus solely on the "cosmic", to its detriment. The challenges of Dostoevsky (or Qureshi-Hurst, but I am not familiar with her work) are not about whether "cosmic" unfairness can have some rationale, but about this suffering person here -- and for that person, notions of some "Divine Plan" (in whatever terms we may conceive of such) do not provide any relief. Religions that include belief in such things as angels or Divine incarnations face an even more stark problem from the lack of intervention; or rather, the lack of inconsistent intervention, by those spiritual powers.
A thought for a possible "version 2" would be to make them capable of reporting a push via Bluetooth or Wi-Fi, to track the action the button represents.
It seems one is missing: "Blessed are those who hunger and thirst after righteousness".
And it is worth noting that there are, of course, many previous expositions on the Beatitudes, which, along with the expected focus on eternal rewards as outranking earthly ones, often provide additional insights, like how the "pure in heart" merit to "see God" because "purity" here means something like "singular focus", which has analogical application to being single-mindedly devoted to a cause, etc.
It is worth noting that, in the religious tradition from which the story originates, it is Moses who commits these previously-oral stories to writing, and does so in the context of a continued oral tradition which is intended to exist in parallel with the writings. On their own, the writings are not meant to be complete, both in order to limit more advanced teachings to those deemed ready for them, as well as to provide occasion to seek out the deeper meanings, for those with the right sort of character to do so.
This would seem related to the notion that "Nature abhors a vacuum", and to the thesis of 'Meditations on Moloch', and to Ilya Prigogine's concept of "Dissipative Structures"... Perhaps one could simply say that it is a natural result of the interplay between entropy and various systems which 'fight' against it.
It may be worth noting that traditionally, Jesus is depicted as being in agreement with Siddhartha here, having emptied Hades before exiting the tomb alive again. This is further emphasized in a sermon preached ~1600 years ago by John Chrysostom, and repeated every Easter in Orthodox (& some Catholic) churches, which includes the line "Christ is risen, and not one dead remains in the grave." Though in combination with other beliefs about Hades/Hell, it seems the intended meaning is that everyone was/is given the option to "ascend", but perhaps not everyone chooses to take it.
These reasons seem drawn from a very individualistic, modern perspective. From a historical, more community-driven perspective, it seems that two other major reasons would be: