Sure. You can make your regular site not a piece of crap. AMP is really just a straitjacket for web publishers. You can make your own straitjacket.
Unless I am missing something in these examples: https://github.com/ampproject/amphtml/tree/master/examples
You can certainly write HTML that doesn't do anything of the things that AMP prohibits, but if it's hosted on a slow server, your users won't get the lightning-fast experience. By caching the pages, Google takes the quality of a publisher's host out-of the equation. (In fact, since the pages are being cached anyway, publishers probably have less of an incentive to invest in speedy server rendering.)
(This is my understanding. I don't work on AMP.)
This is a massive landgrab by Google that only incidentally solves a real performance problem on the web.