The only valid criticism appears to be how google displays search results using its own URL and this toolbar – it seems to break rather fundamental assumption about http and has the potential to break all sorts of tools that rely on the established structure of the web and open standards, as has already happened with the refer(r)er as mentioned in this response.
I wonder if there's a way to get the same result without rehosting content on their own URL. Couldn't they allow publishers to achieve the same result with a CNAME, possibly for amp.<hostname>.<tld>? And do the google servers add anything beyond being distributed caches? Because if not, it seems this level of indirection is redundant for websites already hosted on CDNs.
Regarding the toolbar: yeah, that's a terrible idea. I have no sympathy for publishers who object to it because if it reduces your retention rates there's probably more wrong with the content than the presentation. But as a user, it's the sort of "assisted browsing" that feels intrusive, like resizing the window or a "you need flash" popup (I don't).
Considering their market share in browsers isn't far behind the in search, I wonder why that function isn't just a chrome feature. Funny thing is: it's a feature that exists in Safari ("Search results snapback").