I don’t want to speculate
too much on the legals of the situation, so I won’t talk about anticompetitive matters.
As for why not do this in indexing, of course they’re doing that. They’ve been doing that for a very long time, but that approach can only go so far. There’s a constant cat and mouse game between websites and search providers, and AMP is a way to end it once and for all.
It’s important to stress that the motivation here is largely user-focused. People tend to ascribe to Google these shady Oracle-like motivations around screwing users and developers, but the truth is that moves like this are largely motivated by a desire to improve the experience. Not out of any sort of altruism, mind you, but because what’s good for the user is generally good for Google.