Yeah, not.  Your list of things requiring a license are not listed as Constitutional Rights.  Do you need a license to have legal representation?  Or a license to not be subjected to warrantless searches at the whim of government?  How about that license to have a speedy trial, or maybe even a license to worship as you please.  These things are not negotiable, I doubt you would trade them for a misguided sense of whatever you think it will accomplish.  The felony/domestic violence thing is already in force; you can't own/possess a gun with either.  There are stiff federal penalties for selling firearms as a dealer without a Federal Firearms License.  With your idea, regular citizens get the shaft, and the criminals laugh all the way to what ever crime they can commit with a gun, stolen or obtained on the black market, outside the purview of your license.