Super interesting post.
You illustrate a scenario where someone has consentual sex with a child (so far so good).
You mention that rape accusations could follow, but you also acknowledge that this can also happen with grownups. OK, maybe the chance is higher with children.
I'm not sure I actually see the problem of false rape accusations at this time, especially given the current situation with the age of consent (aoc) being way too high. Right now there's no legal sex with those underaged at all. Lowering/removing the aoc will at least allow legal sex with younger people which would be a huge step forward.
But only after that it becomes important to think about false rape accusations, so that only once the aoc goes down, it will be up to the girl lovers to be extra careful. You can think of ways in which to minimize risk up until even recording audio of the two of you mentioning that you're about to do it with consent. It sounds weird but I can't imagine a court wouldn't use that as evidence (but I am no lawyer/judge).
I'm inferring from your 7th paragraph ("If you believe that...") that your alternative is to not require consent. In this way rape would not legally exist, although of course it would exist in real life. You propose that rape should not be illegal. I don't know exactly how to answer this, and the only reason I want to is just in case someone agrees with you. I don't know how to explain it but it just makes sense to me that in any love-interaction between two people, both should want it. If you have a rape fantasy then I don't know how to deal with that but I think most girl lovers don't want to rape girls and would much rather have the girl enjoy it willingly as well, so I basically just don't see this as a viable option and you'll have to argue better for why you think legalizing rape will be good.
If the age of consent is removed, there will be a change in:
1. the number of positive sexual interactions between people and previously-underaged (i.e., both consent and like it)
2. the number of negative sexual interactions between people and previously-underaged (i.e., at least one either doesn't consent or doesn't like it, this includes rape and false rape accusations)
So you say it is more likely for 2 to go up than down but of course 1 will also go up, so the question is which will go up more and how to weigh this. Anyone who would lower/remove aoc will probably think that 1 will go up more than 2, anyone who would leave aoc as it is will probably fear 2 going up way more than 1, and probably doesn't believe 1 even exists or is possible.
Allowing rape.... I just don't see how to fit that into the way I think about these things so I can't wrap my head around it but feel free to enlighten me.