I wonder if this is related to the first party cookie security model. That is supposedly why Google switched maps from maps.google.com to www.google.com/maps. Running everything off a single subdomain of a single root domain should allow better pooling of data.

Google owns the .google TLD, could they theoretically use https://google or is that not allowed?

Not allowed for gTLDs. Some ccTLDs do it, http://ai/ resolved as recently as a year ago though I can't get it to right now.

You need a dot at the end for it to resolve correctly

https://ai.

It’s unreachable anyway

Going by the Wayback Machine it looks like it used to redirect to http://www.ai, which still works, but only over HTTP.

Well of course http://www.ai would work. That's no different from http://foo.ai .

http://uz./ serves a 500 error.

Not sure if that’s allowed, but that sure feels like a throwback to AOL keywords if it was — just at the DNS level.

Could still do keywords in Chrome, as they control the browser.

This is so they can use the same tracking cookies across all their products.

I think they probably know what they are doing.