Let's take this a step further. This issue is presented as one of those balancing acts: The privacy of lawful gun owners, we're told, must be balanced by the people's "right to know" and the need to hold government accountable. But the only reason that governments have lists of gun owners is that they require licenses or concealed-carry permits. The right to self-defense, and therefore the right to buy and carry a handgun (the most effective means of self-defense), should require no one's permission. It is a natural right. The Second Amendment didn't invent the right to own guns. It merely recognizes it: "(T)he right of the people to keep and bear arms shall not be infringed." It doesn't say, "The people shall have the right to keep and bear arms."
Alaska, Arizona, Wyoming and Vermont recognize this right and require no permits to carry guns. (Montana also has this policy in all but a few urban areas.)
Unfortunately, the Supreme Court, while striking down outright bans on handguns, left room for permits. But it's hard to see how that is consistent with the natural right of self-defense.
I leave aside whether a felon who has served his sentence should be deprived of the means of self-defense because there's a more practical point: Gun laws have no effect on people who plan to break other, more serious laws. Guns are the tools of the criminal trade. If people in that business can't get them legally, they'll get them in the black market. And where there is prohibition, there will always been a black market.
The law of supply and demand is as reliable as the law of gravity.
I say we reject the premise that the state can legitimately exercise this power at all. What would Thomas Jefferson have said about gun permits?