No, it isn't. But stooping to insulting terms like "juvenile" is frequently what gun controllers are reduced to when they find themselves unable to make a logical, fact-based argument.
Well, first we'd have to get to an agreed definition of "arsenal," but the three you list hardly comprise one. There are, in fact, many good reasons to own far more guns than that, as guns are quite specialized for different purposes. At the moment, I think I have about 20, and each has different and specific purposes.
But that's beside the point. Bear in mind that we have a Bill of Rights, not a Bill of Needs. Please try applying your argument to any other enumerated right and see if it holds water. (Does anyone really need more than 3 books? Or need to post to a forum more than 3 times per day?) The argument to limit the number of guns a citizen can own is silly, as there is no compelling and demonstrable justification that it will in any way reduce crime. Furthermore, it is entirely impossible to implement such a restriction without setting aside most of the rest of the Constitution.
Does the right encompass the ability to overthrow a tyrannical government? Because that was the original reason for it. Such an ability today would require much more than the three weapons you seem to think are sufficient.
Also, please consider that the Constitution doesn't "let" us do anything. It restricts the Government. There's a profound difference between those two things, and a US citizen should hold that difference dear.
Again, we don't have a Bill of Needs. We have rights, and many of us are quite serious about preserving them.
But if you don't like this particular right, the Constitution can be amended. Have at it. Good luck.