The page is still yours. You have absolute control over the branding, the analytics, the monetisation. Just because it happens not to be served from your domain doesn't mean it's not yours.
Let's also not forget that AMP is actively encouraging alternative caches: Cloudflare Ampersand[1] was announced literally an hour after my post. It's a whitelabelled AMP cache aimed at solving this exact problem.
Yes you still control most of it. My argument is that the traffic /would/ be going to your actual site (where you aren't limited at all) but now it is going to a google AMP page with strict limitations. Which isn't great, but the big deal is that bar on top that doesn't link to your site. That is so bad for your site and massively increases the bounce rate.
That is a sticking point for me. Alternative AMP caches (with alternative UX, e.g. Ampersand generally keeps users on your site when they bounce) go some way towards solving this, but they're not (yet?) first-class ecosystem citizens:
> But these are just guidelines, and Google can’t guarantee they’re behaving well, so they’re not first-class citizens.
> I’d love for this to be something you could statically verify, just like AMP HTML, so that anybody could add a Cache to the ecosystem and get a lightning bolt on Google search results and Cloudflare links and Twitter Moments™, but I’m pretty sure this reduces to the Halting Problem.
AMP is a PROXY/MITM service, with all the perks that come from being such a service. There is nothing stopping google ,or whatever company owns them after they become a Yahoo!, from changing their "policy" to better be aligned with their interests.
