For sure, you can do PGP, but if it's decades old, you have to ask yourself: Why hasn't public key cryptography taken off as a sign in solution in the same way that email or Google or Facebook have been?
Mainly because it's always been a chicken and egg problem for consumers and application developers. If you implement PGP as your sign-in method, it's unlikely that any consumers will adopt it unless they're developers. And you increase the barrier to entry for anyone who does not understand it.
In the case of MetaMask, this has already got significant traction at 21 million monthly active users (more if you count other EVM wallet solutions), because there's no other way to interact with a blockchain. It's also relatively user friendly. And there's an ecosystem now of applications that require it for interaction, so you're starting to see network effects grow for "Sign in With Ethereum/EVM".
> But successful internet communities do everything in their power to remain walled gardens
This will be proven to be false in the long run. This was the same argument against Linux back in the day vs. Windows. The bazaar will win against the cathedral in the end.