Being generous, maybe half of users can look at a URL and immediately identify the domain they are on. That's terrible, and goes a long way to explaining why phishing attacks are so prevalent.
I'm actually pretty excited to see what they come up with. If it's even marginally better than what we have now I'd be all for it. I'm guessing they'll end up showing some combination of the domain and page title by default (which might incentivize more sites to FIX THEIR GODDAM TITLE SCHEMES!).
I can see the future now: User enters his target (mybank) into the Google search bar on his Google Android device, the device opens Google Chrome with the Google amp page form mybank already loaded. The user never has to worry about urls or where exactly he is entering his banking information and login critera. Google makes everything a clean and seamless experience and user never has to leave its warm embrance.
In all seriousness, I have no doubt this is due largely to Google's frustration at Ad Blockers. If there is no URL, and you're in the Google Garden protocol, there is no way to block ads, or at least no way to NOT download them.