The overlap here is the centralization of identity, not the actual real name part. Is it desirable to have my hn handle also match my wow character name?
Who said you need to only have one ENS name either? You could have one that you use for personal tech-related stuff, one that you use for work stuff, one that you use for gaming-related stuff, etc. (although for that kind of usage to really take off, Gas fees will need to come down).
It’s not about storing your public key, it’s about storing your username and the fact that you (the owner of that key pair) exclusively own that username (for any system that federates with ENS).
Your public key is available to everyone on the internet so anyone can verify your signed message. You can't do that without a blockchain unless a trusted third party is used.