You still need to store that data on somewhere to verify if someone owns a membership and whether it is valid though (memberships can expire).
That data is stored on blockchain vs having a centralized database. Refer to an earlier comment for why having it public is useful.
As for why people didn't use certificates till now, I don't know. I know they use wallet connect more which operates on the same principle but with existing adoption.
...why do you have to have a peer-to-peer network managing a blockchain just to verify membership data? It would be simpler to just have whoever controls memberships sign a user's public key to indicate membership (and then you add some metadata for expirations/membership levels/etc.). A user seeking to assert membership presents that certificate and proves knowledge of the private key.
Really though, I am not sure what problem is being solved here. Why do we need this in the first place? What is the attack scenario we are trying to address?
That data is stored on blockchain vs having a centralized database. Refer to an earlier comment for why having it public is useful.
As for why people didn't use certificates till now, I don't know. I know they use wallet connect more which operates on the same principle but with existing adoption.