They already serve informational purpose at best, the site belongs to a tld with certain restrictions, but why tld restrictions should be expressed in the domain name?
TLDs can be thought of as namespaces, and they have good reason to exist.
For one thing, changing how domains work like this would massively drive up the cost of any one domain to the point where hobbyists and open-source projects would be priced out. I have a few domains, none of which are duplicated across different TLDs, and each of which serves a different purpose. It would have been pretty much impossible for me to do this if everything was under one namespace.
In addition to the price aspect, it would pretty much force the system into being a much more restrictive version of the already-existing trademark system - except that there wouldn't even be any exceptions for different fields, as there is in the current trademark system. For example, one of my domains coincidentally (and unknowingly at the time I registered it over 20 years ago) collides with the name of a movie. It's in a completely different field (actually, it's a personal, non-commercial site for me and not much is public on it) but I almost certainly wouldn't have been able to get it if TLDs didn't exist.
If you have no duplicates, why can't you have them under one namespace? Namespaces are supposed to separate duplicates so that they don't conflict. Without duplicates namespaces don't serve their purpose. TLDs can be kept as a supplementary technical information, like, e.g. cname.
But there are duplicates. There are a vast number of cases where a domain name under one TLD isn't held by the same person/company who holds the same domain name under another TLD.
