This prohibition only applies to gTLDs. It does not apply to ccTLDs.

http://ai./ is a better example.

HN doesn't like your link's formatting. Try: http://www.pn./ or http://www.pn/

Your .pn link doesn't work for me without www part.

At least for https://www.fi/ the case is that someone registered "www" as the domain name in the early days.

Missed opportunity for ny.ny

The reasons why these don't work go much belong policy. Let's say that you're trying to advertise city social services in a subway ad campaign; how in the world do you get people to go to just "nyc" as the domain name? I guarantee you most of them will end up just performing a search on "nyc". It simply doesn't work. When you put nyc.gov as the domain name, everyone knows what that is and how to navigate to it.

Secondly, we have the expectation that subdomains of a given domain are run by the same entity, and represent natural semantic subdivisions. E.g. there's google.com, the over-arching website for all of Google and its first major product, and then for its other major products there's maps.google.com, mail.google.com, docs.google.com, etc.

This doesn't work with nyc, because subdomains of nyc are actually registrable domain names all their own that are controlled by other entities. So you can't have nyc be the overarching website for NYC, and then have parks.nyc, housing.nyc, business.nyc, etc., as natural subdivisions of it, because other people can own those domain names! So now you have no great way to subdivide up your site, and other people's sites are easily confusable as yours.

The only real way to do a dotless root DNS website is if you control the entire TLD; it has to be closed and not open to registration by external parties.