Ah, I forgot about that and never really considered it because GPG is so annoying to use, but it is fairly reasonable.
I don’t see how it has too many advantages (for the internet) over creating your own CA. If you have a mutually trusted group of people, then they can all share the private key and sign whatever they trust.
I think the main problem is that it doesn’t scale. If party A and party B who have never communicated before want to communicate securely (let’s say from completely different countries), there’s no way they would be able to without a bridge. With central TLS, despite the downsides, that is seamless.
There's issues with it, but it is an alternative model, and I could see it being made to work.