I think you'd be assigning too much importance to subject agreement between connected clauses as a grammatical phenomenon if it crossed your mind even for a second. You are free to pick whatever subject you think is fit according to what makes pragmatic sense and your preference. So the subject agreement in 「褒めてもらっても何も出さないよ」 does not make it preferable to the other two in terms of grammar, and it's just wordier without an apparent merit.
「褒めても何も出ないよ」 is a highly idiomaticized expression, so people use it without thinking about its literal sense, but I understand your feeling that the speaker's using 「何も出ない」, thus effacing their own agency in the situation, is somewhat unexpected. It sounds as if they were talking about some mechanism (an inanimate thing, hence better compatibility with 「何も出ない」) that automatically gave out something in response to a certain stimulus. I think it wouldn't be too far-fetched to imagine that the prototypical utterance of this phrase was a jocular metaphor where the speaker was comparing themself to something like a vending machine (it could be anything, or nothing specific -- just a vague allusion to some kind of non-human quid-pro-quo mechanism), where you put your money in and it gives you a goodie in return.
On the practical usage front, there's some difference in nuance between 「褒めても何も出ないよ」 and 「褒めても何も出さないよ」. The former goes like "You won't get you anything flattering me, you know.", and the latter like "I won't give you anything even if you flatter me, you know.".
I'm not entirely sure if the translations make things clearer, but my main point is that 「褒めても何も出ないよ」 sounds more non-personal and humorous, while 「褒めても何も出さないよ」 possibly might sound a tad bit more like a refusal, like the speaker thought the flatterer were really trying to get something out of them. That maybe partly why the former is preferred.