When you see how far they've stretched the "interstate commerce" clause, I think your proposal would only lead to a greater mess. Besides, people want laws that create simple rules like when can I carry this gun? Who, when, what, how, where are easy and categorical, why is often vaguely defined in someone's mind. For example if you say the "mission" is for self-defense then anyone caught with a gun can always claim that, even when it seems extremely unlikely.
I'd just start throwing lots of question at that definition until you got it narrowed down.
"A well regulated Militia, being necessary to the security of a free State, the right of the people to keep and bear Arms, shall not be infringed."
Who are "the people"? Is it the same "people" who have the right to a fair trial? Because I'm pretty sure that includes everyone, not just citizens or residents but that illegal immigrant crossing over from Mexico too. Does he have a right to "keep and bear arms"? Does anyone not connected to any milita? Even back then the militia was all "able bodied men", is a woman or a cripple protected? What about minors? The mentally ill? Felons? They all have the right to a fair trial, no ifs or buts about that. Can you condition this right on a license or registration or test? Can you deny anyone to buy a gun or place restrictions on those selling guns like mandatory waiting periods or is that denying them the right to have a gun like right now? Can you regulate how it's stored without violating the right to keep it, like keeping it dismantled, unloaded, ammo separate from gun, in a gun locker etc. because really you could demand it be encased in three feet of cement. What does it mean to bear arms, does it mean openly or concealed, can you have it in the glove box or under your seat? Can you carry it on private property, public property, in public buildings, on other people's private property that's open to the general public? What exactly does "arms" means, is it the right to have cannons and nukes or small arms? Poisoned darts, is that arms? What about knives or tazers or and any other non-gun "arms"?
Those are just off the top of my head, it wouldn't be that hard to make a law that actually answers all of these questions and it would lay most the issues at rest without ever going into the tricky question of why you might want to have a gun.