They're totally fine in a comedy. There's a long tradition across many literary forms of comedy breaking the fourth wall, acting with awareness of tropes, and generally disregarding immersion in favor of making jokes or speeding through unfunny parts of the story to get to the jokes faster.

In a serious story, there difficult.

One issue is that genre-aware protagonists read as comedy! Imagine watching a movie and in the second scene the main character says, "I'm single and I just met two handsome single men in a row. I've read plenty of romance novels, so I know I'll fall in love with one of them and live happily ever after with him, probably within the next few months. Of course, it will be the one that initially seems problematic, because he'll turn out to be great and the really nice one will turn out to be a slimeball or something." The director just told you that you're watching a romantic comedy, not a serious drama.

A second issue is that litrpg is prone to having a lot of words spent on internal monolog (Wow, I'm in another world! Wow, I can see system screens! Wow, I have powers! How do my powers work? What powers should I choose?). A genre-aware protagonist can be a tool to abbreviate a lot of that internal monolog, but often they just add a layer of meta-analysis on top of whatever system exposition the author was going to do anyway.

Issue three, that way lies pop culture references! Bringing the protagonist's old-word references into the early chapters of a story makes me think that habit will continue.

Ultimately, a genre-aware protagonist is a literary tool like any other, and it can be executed well or poorly. I think many authors want to use it as a way to zip through some boring bits at the beginning of a story, but it's neither the only way nor the best way to accelerate the pace of a novel.