Are you against a universal registry through ATF that can only be accessed by law enforcement? (nothing like this currently exists before you assume)
If by universal registry, you simply mean a registry of people who are legally registered to own a firearm? Sure. No problem at all. I just proposed an idea where anyone can get a gun registration ID that verifies that they are legally allowed to own firearms. You do that once. The cards are required to purchase any firearm. The POS systems are linked to a database that validates the card, so that if the persons legal status changes, they can't buy guns. Beyond that, no tracking of anything at all. It would act like a credit check. You either can or can't legally own a weapon.
No background checks required because it's already done for you. Swipe your card. Green means you can buy a gun. No need for bewildering registration or licensing systems for the firearms themselves. If you are in possession of a firearm, cop swipes your card. Green means you're legal and you continue on your way. Point being as long as the firearms themselves are legal to own (ie: don't violate existing restrictions), there's no need to track how many anyone has or what types they are within that range. In exactly the same way that if I'm legally able to buy alcohol, the government shouldn't be tracking how many bottles I buy, or what kind. If I want to buy 20 television sets, the government shouldn't track that either. See how that works? If I want to give a friend of mine a gun, as long as he's got a valid card, it's legal. There's no more need to track that than there is whether I give that friend an old dresser I don't need anymore.
We track way too many things already IMO.