1) Performance - Yes, it LOADS fast, but MANY pages "feel" janky, when scrolling, especially pages that allow you to load additional accords by scrolling left/right. Only the simplest pages don't "jank" on my device.
2) Scrolling - It isn't the native scroll. It seems to be a div with "overflow-scrolling" applied. Other than that feeling "off", it prevents the bottom toolbar from hiding, reducing screen real estate.
3) Sharing URLs.
4) Biggest: No way to opt-out. I'm a fan of the open web. It's why I prefer a website to a sandboxed experience you get with native apps. At least for the first click on Google SERP pages, I'm "stuck" with google.com.
One note: I get the AMP use case, and I'm sure there are users who prefer AMP pages for the performance they see. However, I'm fortunate enough to live in an area with decent mobile speed/bandwidth, and loading the original pages are rarely "slow" on my device. However, the originals all address the issues I noted above. I'll take the .5-1 second delay for the original(s), over the AMP version.
I’ve been in mobile development for about a decade, what Google did was re-invent WAP on top of HTML5, turning back the clock at least 10 years.
By also sending all non-Google traffic through the tunnel ("for improved speed!" remember when AOL included SpeedBooster Technology?) they'd control a majority of all non-search internet traffic, like AOL without the disks. And they wouldn't even have to bill you because they'd get an unlimited supply of ad data.
Aside: from a privacy perspective it creeped me the hell out once I realized what was happening.
2) Touching tap to return to the top of a webpage is broken.
3) Searching for a word within a webpage is broken.
This is all basic functionality that I use often. And I'm sure there are other things broken about it.