Royal families have survived much worse scandals, so they'll probably just cut him loose and toss him to the justice-wolves. But he's also the Queens favorite son, so there might be some wagon-circling.
And when the Queen dies (she IS mortal, right? RIGHT?) it's going to get really interesting to see if a Perfect Storm comes together to upend the whole anachronistic inbred sleazy lot of 'em.
I'm obviously not a fan of "royalty" (the concept nor those involved), and don't otherwise follow their going's on except when it looks like they might be poised "to go through some things" which is worth pulling up a chair and making some popcorn for.
I mean, since we're talking about finding justice for sex-trafficked minors then to hell with anyone involved with that as well as any who were technically 'innocent' but looked the other way. Which I get the impression is probably most of them. Harry could probably see what was coming and got out while the getting was good.
It sounds like soap opera bullshit to talk about, but they are a real mostly-symbolic-but-also-not Monarchy with vast wealth and influence in the real world, so their collapse will be a big deal.
France seems to do okay without one, lol. Tourists will still come to gawk at the castles 'n' shit even if there are no antiquated, cosplaying perverts living in them.