PGP’s web of trust was kinda bad privacy-wise in some regards, as it basically revealed your IRL social network.

If my PGP public key has 6 signatures and they’re all members of the East Manitoba Arch Linux User Group, you can probably work out pretty easily which Michael T I am.

Are there successful newer designs, which avoid this problem?

The IRL social network is actually the important part of the trust structure.

The only one of these I've seen that really worked was the Debian developer version: you had to meet another Debian developer IRL, prove your identity, and only then could you get the key signed and join the club.