Review
When this phrase is used it is maybe implied that the equilibriating happens much faster and further than the actor (usually a democratic regulating body) expected, and that they are too slow to "evaluate medium term, make corrections".
One other potential benefit of an unstable mechanism is that there is no energy loss that comes with damping, in other words the many possible errors are not rejected as heat. Instead, the error can be measured with a much smaller energy cost, and then a reversible correction can be made that on average costs no energy. In concrete terms this can be pictured as replacing a dashpot or a shock absorber with a finely controlled quick response linear electric motor (one that can reproduce and correct any error that occurs). Of course a dashpot-like solution is usually simpler and more reliable. I have come to appreciate reliability even more as I've grown older.
Oh, there are absolutely correct places to use the phrase and correct places to benefit from reliable simplicity! My main argument is against mindless usage that I unfortunately witness nowadays a lot. Understanding why and when we need to solve for the equilibrium in evaluation replaced by the simple belief in a rule that we should - always and for everything.
TLDR: "Solve for the equilibrium" is a nice sentiment, but shouldn't be applied mindlessly, it's not nearly as universal approach as some think.
Longer version:
The phrase "you must solve for the equilibrium" when evaluating something became almost like mantra and a lot of people use it automatically without stopping and thinking.
Do you though? Do you really? Or is it just a fancy way of saying "mind the consequences" (which it shouldn't be)?
"Solve for equilibrium" just tells you what the situation will become if you assume this one action, this one rule, and then let the system achieve equilibrium without additional interventions. When and what real system ever works like this? Those that I encounter daily are mostly "achieve short term results, evaluate medium term, make corrections before equilibrium sets".
The result of the equilibrium solution just tells you the most stable outcome that, when achieved, will try to maintain itself against future interventions. Quite famously in the classic prisoner dilemma the Nash equilibrium result is the worst one for all involved.
There are cases where you want stability, but this isn't nearly universal rule! Modern fighter planes by themselves has the stability of the brick and require thousands micro-corrections from the onboard computers every second. But the same instability grants them incredible maneuvering capabilities, which their more stable older relatives can't pull off, as their "solved for (aerodynamic) equilibrium" air frames would fight against them.
In a chemical sense every steel tool "solved for equilibrium" is a pile of rust. Unless you regularly support it - and even then it's still a pile of rust, just much further down the line. And when that happens - it doesn't make the tool retrospectively useless, you just replace it.
There is nothing wrong in the systems that require constant corrections as long as