We have the Constitutionally protected right to keep and bear arms, not to keep and bear only certain specific weapons. Just like we have the protected right to freedom of the press, not freedom to print something on only a movable type hand powered printing press.
Too often this discussion gets parsed into the mind-frame of "do you NEED such and such weapon"; or "Why do you need such-n-such", when the real weight should be in the opposite direction. Because our Constitution declares that the citizens have the Right to keep and bear arms, and forbids the government to infringe upon that inherent Right, if the state desires to do so, it must have an overwhelmingly compelling, and specific, argument to be able to do so. There is no overwhelmingly compelling argument for banning ALL the US citizens from owning any of those specified weapons. Frankly I don't think that most of the existing gun ownership laws (and many other of our laws in fact)are within the intention of the Constitution.
As I've said before I agree that there are some common sense limitations that could exist. However, the attempted method of implementing them is horribly flawed. We can not let Congress pass laws the limit one of our Constitutionally protected Rights, because it seemed like a good idea at the time. By doing so we are opening the door for them to limit ANY of those other protected rights. IF someone feels that one of those Rights should be reduced in scope, then they need to make a much better argument, and get an amendment to our Constitution passed, not just pass an ordinary law.
We let it happen in the 30s from the fear of the mafia when the federal government virtually banned the real assault (fully automatic) weapons. In order to own one you must pay for an expensive federal license (as well as other heavy restrictions). If owning property, or paying a poll tax, infringes on a citizens Constitutional right to vote in an election, then an expensive federal license does the same thing to keeping an bearing arms.