Just because it is an arm does not mean it is needed to be able to bear arms.
The Constitution protects the right to freedom of speech but I do not have the right to scream in your ear even though that is a type of speech.
Moreover, it would clearly be Constitutional to ban guns that had a propensity to blow up in the user's hands, injuring him and his fellow shooters.
The government could also ban the import of certain guns to protect domestic manufacturers. You do not have a right to either a Norinco or an H&K.
Ok one last time, and then I'm done...
Firstly you did read the intended use of an Uzi, that was posted earlier, I assume.
Ok so why do you NEED an M16... you most likely won't in your lifetime. Why do you NEED a handgun... same deal. You may argue you NEED them for defense, suppose we took the approach that indeed you may, however if after 10 years you cannot provide evidence that they have been used in defense by way of a police report we can safely assume that you're not at risk and thus no longer need them for defense. After that you can only own a 22LR. There ya go... I mean I didn't eliminate your 2nd amendment rights, you only needed those weapons for defense which patently you over estimated the risk of.
By taking the approach you suggest, then the government could issue an approved list of firearms, it would not impact your second amendment rights, it would undercut the purpose of the 2nd amendment however. The same could be said about cars too, you don't need a Ferrari, or even a stationwagon if you don't have a business or kids.
By placing arbitrary and ill defined restraints on a right you eliminate the right it becomes a privilege. For instance you use yelling in someone's ear impacts your 1st amendment right, what you say will not get you prosecuted, if you injure the person for instance rupture their eardrum you could be prosecuted for most likely assault it's a right to free speech, not a right to yelling in someone's ear. However is banning handguns legal, no, DC vs Heller, but not allowing someone to shoot off a full mag for the hell of it in public, that too is illegal and will get you prosecuted it's a right to keep and bear arms, not a right to shoot up the local mall.
Free speech, freedom of religion, freedom of the press, freedom to assemble and petition your government and to bear arms. Are all recognized as natural rights. Suppose legislation was passed that only allowed assembly on every other Thursday. It's no longer a right, you now have the privilege of assembly on every other Thursday. By being a natural right, you can do it any time with anything you want, your dime your choice. As long as it doesn't come into conflict with others rights.
As to Uzi's any SMG (with full auto capability) makes an excellent home defense weapon, it's short, easy to handle and quick moving, low recoil and accurate enough at the range needed, and with burst fire more than able to deal with multiple threats, which is why it's the weapon of choice of most SF doing house clearance. I'd argue that for most self defense purposes you're likely to run across as a civilian that an SMG like the Uzi would be the weapon of choice over an M16 or an M4, of course it's not in common use due to the Hughes amendment, so people are using handguns, M4gerys and AR15's instead. However eliminate burst or full auto and an SMG is most often an oversized high capacity handgun.
Now as to banning specific items likely Manufacturer Model and variant because of bad manufacture, or imposing import restrictions. Both of these are within federal government scope, one for safety reasons, one for economic. However what the feds cannot do, is ban all firearms for safety reasons, or impose import restrictions while eliminating firearm manufacture in the US. Now HK you'd have an issue, since they have a manufacturing plant in the US, I don't know about Norinco.
Hope you got the information you wanted, because I won't be replying to you again.
