Which EU-based government(s), though? The implication I get is that is under your proposal, the dev(s) would have to register with almost every EU countries out there.
Well no, the store/Google/Apple would need to support entering compatible data with all systems, like with addresses or phone numbers and doing any integration to verify data if need be.
Each dev would only be in the registry of their own country, as they already need to be for tax related reasons anyway. I'm not sure why we need duplicated databases.