If someone goes to jail for shooting someone or for taking a gun and sticking up a liquor store or for any other violent crime then I'm not sure I want them to be able to carry a firearm when they get out. You, on the other hand, may disagree and there nothing wrong with that. I may want a person getting a concealed carry permit to go through a training course before being issued the permit. You, on the other hand, may feel that such training isn't necessary and that's fine, too. I may not be comfortable with people being free to bring a concealed firearm into a police station or a football stadium. Again, you may disagree and there is nothing wrong with that. But in any case, if any sort of restriction is to be placed on who can carry a gun and where I'd rather those restrictions were made at the state level and not the federal. This law goes against that.
I'm concerned about that aspect too. As others have pointed out upthread, the thin edge of the federal wedge is a dangerous thing to let in here for the first time, even if the immediate intent is good. I'm left with the conundrum of what to do in cases where individual states are violating a baseline level of civil rights. Two ideas present themselves.
Do nothing. Let the tyrannical states drive away all their worthwhile citizens into the arms of states that treat them like they are the engine driving the success of the state. (See California)
Or if action (as opposed to inaction) on the federal level is the best way to go, maybe do it judicially, by saying the states are violating the civil rights of visitors from other states and that they're not allowed to do that.
Anyway, I do agree that opening the door to the idea that federal legislation on this issue is even potentially legitimate is worrisome. Hard to get back in the box once you let it out.
I'd strike the words "carry a firearm when they". Some individuals will pose a danger to the public if they not kept under very close supervision (as in a prison), whether or not they are legally allowed to acquire firearms. Other individuals will not pose a danger to the public, whether or not they are legally allowed to acquire firearms. While there are a significant number of people who don't pose much a danger to the public without firearms, but would pose a danger if they had them, the vast majority of those people, while legally allowed to buy a gun, are disinclined to do so; there is thus no need to restrict them.
Thus, even if rules restricting firearm ownership by convicted felons would be constitutionally justifiable, it's unclear that any legitimate good they accomplish would outweigh the illegitimate harm caused when they facilitate the denial of the rights of people who are not accused of having done anything illegal, nor of being incompetent to handle their own affairs.