The problem is there doesn't seem to be a way for the left and right to compromise on this issue. You can't realistically police private party transfers without mandatory registration, and there are too many instances of registration later leading to confiscation for that to be palatable to 2nd Amendment rights advocates.

On the other side, there have been several attempts to open up access to the national background check system to private sellers, but every time it gets blocked by the left, as voluntary background checks are largely seen as an ineffective half measure.