under gTLD rules (the TLDs that private companies can buy/invest in), TLD operators cannot host any records outside of NS and RRSIG/other cryptographic record types, so they can't host email or webpages at the TLD itself. ccTLDs (country code) are effectively "owned" by the nation state themselves so ICANN generally doesn't impose too many rules on how they're used.

https://www.icann.org/en/announcements/details/new-gtld-dotl...

I believe the biggest issue is that it would have to be a non-SSL domain, unless Google figure out someone willing to sign a certificate for a that. But I also remember this being frowned upon by ICANN or some other entity in the past. Btw, the dot is not necessary (maybe it is in some OSs/browsers): http://ai/