Yes, because it's their Constitutional right to do so - keep and BEAR arms, remember? - along with its concomitant responsibilities, which is the unspoken but critical component. You do realize said incompetents currently can legally carry in their homes and vehicles RIGHT NOW, right? That includes grandma who might not be able to see well enough to hit inside the 8-ring at 15 yards but sure as heck can stick a revolver in a rapist's ribs at halitosis range.
When I carried legally for a few decades in South Africa, there was no training course in order to carry - we devoured everything we could read regarding the law of self-defense, knowing full well that what we didn't know would bite us in the behind. A personal anecdote is no proof of anything of consequence, of course, but an entire country made it work so...
You're moving the goalposts here; I wasn't referring to other states at all, but if they "want to travel to another state", that's their problem. Personally I'd like to see mandatory classes gone in every state, yet like most everyone else I'd highly encourage anyone to get as much training as they can in the areas of safe gun-handling and legal issues.