I've always figured that constraining an LLM to speak in any way other than the default way it wants to speak, reduces its intelligence / reasoning capacity, as at least some of its final layers can be used (on a per-token basis) either to reason about what to say, or about how to say it, but not both at once.

(And it's for a similar reason, I think, that deliberative models like rewriting your question in their own terms before reasoning about it. They're decreasing the per-token re-parsing overhead of attending to the prompt [by distilling a paraphrase that obviates any need to attend to the literal words of it], so that some of the initial layers that would either be doing "figure out what the user was trying to say" [i.e. "NLP stuff"] or "figure out what the user meant" [i.e. deliberative-reasoning stuff] — but not both — can focus on the latter.)

I haven't done the exact experiment you'd want to do to verify this effect, i.e. "measuring LLM benchmark scores with vs without an added requirement to respond in a certain speaking style."

But I have (accidentally) done an experiment that's kind of a corollary to it: namely, I've noticed that in the context of LLM collaborative fiction writing / role-playing, the harder the LLM has to reason about what it's saying (i.e. the more facts it needs to attend to), the spottier its adherence to any "output style" or "character voicing" instructions will be.