Well...sort of. It's more of a world building thing. I would expect any character in a fantasy or supernatural book to ruminate on the implications of death if they discovered that there is an after life and that there are numerous ways to return from it. It's not something every story does, but any story that has a curious protagonist is going to eventually ask how the thing they're interacting works. So in that sense, I don't know if Batman acknowledging that he can confirm an afterlife and even interact with it to an extent is the same as him acknowledging his medium....
But the bigger problem here is with superheroes, it actually is a bit different because the nature of mutliple writers writing one character at once and across spans of decades means that comics can never achieve the kind of consistent worldbuilding and story arcs that, for example, books with a single author can. Whatever one author does another can undo, so while Batman can acknowledge that death doesn't really stick in this world, writers are going to have different takes on how death does work, so his understanding of death can't actually be complete, and acknowledging THAT might be acknowledging his medium.
What I mean is, the tropes came first (as you said) because of multiple writers, market demands, and 75 years of continuity, Then the in-universe justifications were stapled on to cover them as readers became more savvy (too savvy!). So it's like - at least, I see it as - a kind of second-hand awareness of the medium.
Despite being completely different, the capes' world is meant to reflect our own. I think characters kind of need to be blind to certain things for it to all work smoothly along the series' continuity and to remain - and I wish I was joking - 'relatable'.
It feels stupid to write, but there's a weird tension between the reality and unreality of major cape stories that I'm not smart enough to pull apart, but if they followed the world building through fully as you suggest, this tension would break and the capes' world would begin to move away from its familiarness. Does that make sense? I dunno.
But that doesn't change the fact that this
is the world he exists in and that's set up around him, as you said. Idefinitely read anything that addressed it. Someone page Dr Morrison!
Either way, any resurrection of Thomas and Martha Wayne should be met with "Hey, so, billionaire parents. Whats with the illegal child labor?"
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Tangentially, I wonder if the reason Robin is forced to wear bright colours is so criminals shoot at him instead of Batman.