At least higher-end LLMs are perfectly capable of making quite substantive logical inferences from data. I'd argue that an LLM is likely to be
better than many other methods if the dataset is small, while other methods will be better once you're dealing with data that pushes the context window.
E.g. I just tested w/ChatGPT, gave it a selection of instructions about playing music, the time and location, and a series of hypothetical responses, and then asked it to deduce what went right and wrong about the response, and it correctly deduced what the user intent I implied was a user that given the time (10pm) and place (the bedroom) and rejection of loud music possibly just preferred calmer music, but who at least wanted something calmer for bedtime.
I also asked it to propose a set of constrained rules, and it proposed rules that'd certainly make me a lot happier by e.g. starting with calmer music if asked an unconstrained "play music" in the evening, and transition artists or genres more aggressively the more the user skips to try to find something the user will stick with.
In other words, you absolutely can get an LLM to look at even very constrained history and get it to apply logic to try to deduce a better set of rules, and you can get it to produce rules in a constrained grammar to inject into the decision making process without having to run everything past the LLM.
While given enough data you can train a model to try to produce the same result, one possible advantage of the above is that it's far easier to introspect. E.g. my ChatGPT session had it suggest a "IF AND THEN " rule. If it got it wrong (maybe I just disliked the specific artists I used in my example, or loved what I asked for instead), then correcting its mistake is far easier if it produces a set of readable rules, and if it's told to e.g. produce something that stays consistent with user-provided rules.
(the scenario I gave it, btw. is based on my very real annoyance with current music recommendation that all to often does fail to take into account things like avoiding abrupt transitions, paying attention to the time of day and volume settings, and changing tack or e.g. asking questions if the user skips multiple tracks in quick succession)