The idea that you are off the radar because you don't own NFA is a stretch at best. I am also far more concerned about being armed when I need it that being on a list because I got my CCW. Unless you buy ALL your guns, ammo, accesories with cash, FTF you could be tracked.

A slightly more serious answer.
The tax paid transfer nature of NFA ownership would make confiscation MORE not less difficult in my opinion.
4473's are FOREVER. The dealer keeps them and ATF has access to them, if the dealer goes out of business they get shipped to the ATF.