In theory, you wouldn’t need to centralised coin minting; you would just need a way to validate whether a user minted coin is valid.
What is valid? Choose a hashing algorithm, make it public, then let people try to find numbers from a published, immutable list. Essentially, mining on safe net - finding the source which hashes to something on the published list (or equation).
Once you have a minted coin, in will already be associated with your private key at mint time. Receivers of the coin could just confirm the hash is valid before accepting it as a valid token.
This would still be anonymous, instant, secure - all the things associated with safe net. There would be no blockchain either.
Ofc, you could have centralised minting instead, with no mining, but you then have trust issues.
Safecoin minted by ‘the network’ is arguably the best of both worlds. However, the above would be an interesting alternative.