No. That's just strawmanning a terrible implementation.
Here's another less terrible one: Public certificates of ID issuers are what's stored on-chain. Individual users have their (potentially locally generated) DIDs cross-signed by an issuer. The only data being stored on-chain is issuer certificates (and potentially further signatures and metadata around them) and this makes it possible to run the whole scheme in a more decentralized fashion.
Here's another less terrible one: Public certificates of ID issuers are what's stored on-chain. Individual users have their (potentially locally generated) DIDs cross-signed by an issuer. The only data being stored on-chain is issuer certificates (and potentially further signatures and metadata around them) and this makes it possible to run the whole scheme in a more decentralized fashion.