Let's Clarify Some Misunderstandings Around Sign in with Apple
aaronparecki.com
aaronparecki.com
I think the answer is might, probably should, and likely will. Enough apps are cross-platform or share backend code that developers "forced" to include "Sign in with Apple" on iOS may just include it across all their apps/sites. (Especially because they will want iOS users to be able to access their information from desktop browsers.)
It might be a rising tide that lifts all boats in that sense. Especially if Apple keeps their part of the bargain, it might even make sense for non-Apple device users to sign up for an Apple Account/iCloud just to use "Sign in with Apple".
I think that's an interesting question not enough people are thinking about yet.