Hiding the protocol was understandable. For web pages it was 99% http or https, and they could convey which with an icon. (iOS Chrome still shows it for some strange reason). Then mobile Safari dropped everything but the domain name and everyone freaked out. But you can get everything back in Safari by clicking on it, but not on Chrome. Such a simple thing to implement.
If anything they could have just hid the query string, unless it's fairly simple like HN comments pages (item?id=17927972). But with pushstate, you could just hide the ugly bits (tracking, language, etc.) from the user. Take this Chrome promo URL:
https://www.google.com/chrome/whatsnew/?hl=en&brand=CHZQ&utm_source=google.com&utm_medium=homepagepromo&utm_campaign=m69-whatsnew
Using JavaScript, before anything is displayed, simplify it to: www.google.com/chrome/whatsnew
And if you don't like www., don't host at or link to that subdomain!