It's not a tax if it's merely covering the costs of the transaction. That is that if we agree that it is a good thing to require background checks at all, then it will be part of the cost of transferring it.

If you don't agree that background checks are a good idea at all, then just say so.

This proposal is likely a lighter financial burden than either requiring everyone to get a background check for every transfer, or to require everyone go through a federally licensed dealer.

It wouldn't necessarily need to be indefinitely; how long one wants to require this is a policy choice. Long enough to catch repeat offenders is all one really needs; stopping a single person from just once committing any crime is pretty hard.