Do other such methods exist which still allow an trustable verification making identity theft difficult? Are there examples in the Bitcoin/crypto service world?
There are some blockchain solutions that allow verification that you are a real person
(not a bot) without exposing your real identity.
I don't know any other method of verification that is used anywhere, but I guess in theory personal information can be split in several parts, encrypted and kept on blockchain.
That would mean there is no single point of failure, and nothing can be hacked to steal your data, except maybe getting partial information.
IPFS aka InterPlanetary File System, or something similar, could be used for storing information like this.