I don't support private ownership of ICBMs. Sure, you can't afford one anyway, but what about that middle-eastern oil tycoon? He's got the cash handy, and he's got some very passionately speaking friends.
Your middle eastern oil tycoon isn't an American citizen, and therefore has the laws of his own country by which he has chosen to live. He has no rights insofar as the US Constitution is concerned. He cannot buy up an ICBM, and when his sheik comes for his head, tell him that the US Constitution gives him a right to keep and bear any weapon of his choosing.
By the way, you are aware that private ownership of ICBMs is not all that uncommon a thing, aren't you? There is a firm out of California, for example, which bought up a whole mess of former Soviet SS-18 boosters with the intention of using them as launch vehicles for satellites. ICBMs, Sr. Deuce. In private hands, Sr. Deuce.
Are you sure you don't want to re-think your position, Sr. Deuce?
edited to add: By the way, Sr, Deuce, you are aware that in most respects, what you refer to casually as an "anti-aircraft missile" is nearly indistinguishable from a scientific sounding rocket, aren't you? Back in the 1950s and 60s, the Nike series of AA missiles was first established as a series of high altitude scientific research vehicles before it was militarized? Back when I was doing time at the U of Washington - in the early 90s - we had an Engineering lab that kicked out 3-4 high altitude research rockets a month; they looked uncannily like the US Navy's SM-2 'Standard' Anti-Aircraft missile.