Blockchain use case: Criminal History on Chain

I was thinking about a use cases for crypto and wanted to hear some opinions. I was thinking about hitchhiking and if I were to hitchhike it would be nice if I could prove to the person giving me a ride that I wasn't a criminal. There currently isn't anything like this that exists that I know of, without that person running a background check on me then and there which is unrealistic.

So I thought that blockchain could be an easy way to solve this problem. Every crime committed would simply get put on a blockchain and be associated to a key pair. You would need to prove who you were via some centralized service who would provide to you the private keys that are tied to you as an individual. This key would prove your identity and a way to show you have not committed any crimes. You could then present the key to anyone you would want to prove your criminal history to.

I could see this being valuable to companies like Uber or Tinder. That way if you are a driver or a woman looking to go on dates you can be sure the person you are spending time with is not a criminal. It wouldn't be fool proof however it would provide an additional layer of proof for everyone involved.