I realize it. Now, tell me, does anybody have the master keys for those unique addresses? (not the master-key from which they were derived, but the actual key to spend any bitcoin inside them).
Yes, the holder of the master private key. Which isn't us because we don't have access to that.
Great, so what do they use those addresses for? Do they send/receive any bitcoin to it? Nope. You're not using the blockchain in any way, as you have already admitted, so what does this thing have to do with cryptocurrencies?
You could do the same using regular OpenPGP subkeys and registering them in your centralized system. People already use similar cryptographic solutions for all kinds of things (but not pills, because that's pretty silly) so why would they use your service?