This is definitely a valid use case for a blockchain. I’ve several blockchain based digital ID projects out there, though I have not investigated their level of maturity or acceptance. Here’s a few I have found:
https://fractal.id for KYC on exchanges
https://www.digi-id.io/ - Open Auth project based on the DigiByte Blockchain
https://www.civic.com/ - blockchain-powered decentralized authentication solutions, reusable identity elements & KYC
https://www.accenture.com/us-en/insight-blockchain-id2020 - Accenture has joined the ID2020 alliance and leverages its unique identity service platform.

There’s another one that interested me, but I don’t remember it now , but as you can see, there a lot of projects going after that birch as well...