As long as incorporated cities are allowed to exist, they can implement measures such as buybacks, since it is explicitly a local issue and cities can make expenditures. I don't see how it can be enforced.
Considering that some of these buybacks are financed heavily by the private sector I don't see how Constitutionally the state can come in and say what you do with the guy once you buy it off someone. If I was a billionaire I would fund one of these buybacks and destroy the guns just to see what happens. Just from the point of view of small unintrusive government this is crazy. It really demonstrates another fable about small government Republicans. It joins fables about Republicans managing the economy and the military as well.
This is interesting though. It's funny to watch tea party bozos waste their money rallying in Washington when a lot of the really intrusive and dumb regulations happen on the state and local level.
Once you get to a certain level of sales or purchases of guns, you are considered a dealer under Federal law. Keep in mind that one attraction of these buybacks is that guns which are stolen, or which the person who held them should not have had can be disposed of anonymously, which I am doubtful that a Federally registered dealer could do. Basically, the government sanction is needed here to do this, even if someone else provides the money.
Now that I think of it, has anyone checked to see if there is a surge in gun thefts shortly before these buybacks? Seems like a fairly perfect crime assuming you don't get caught doing the stealing since you can be reasonably certain that the fence you sell the goods too won't be turning you in.