The whole point of using a weak model for solving some problem is to trade _off_ some optimality for other characteristics. If you have something that is provably optimal it is probably special-purpose, or requires upfront training or doesn't work in the full generality of cases etc. The selling point of this class of model is that inference is fast and cheap and they produce results that are good enough for a wide class of classification problems where training a real classifier is inconvenient. For example, I have one of these type of models running locally and doing model selection when I use my coding harness. It takes prompts I provide and subtasks spawned by agents and matches those into various categories ("trivial", "research", "implementation", "hard") which are defined by prompts. As you can see this is a very fuzzy task and a "provably optimal" solution is likely impossible to achieve but also would require training on a data set I don't have (a representative sample of possible prompts and subtasks in the various categories).

The decisions it's making are good enough to save me a ton of money on my development so are perfectly adequate for this task.