A great deal of study has been done on this and shows quite strongly that the decrease in criminally held guns happens quikly when the penalty for being caught with an illegal gun becomes severe.. IN locales where the penalty for being caught with an illegal gun is an extremely long incarceration, the instances of people walking around with illegal guns drops precipitously, while in places where the risk of walking around with it is weeks or months of jailtime or easy getting off on the charges, there are many more cases.
Your argument is a straw man, because it assumes no action whatsover on sellers (we have a LOT we can do here) and no action whatsoever on penalties for possession (we have a LOT we can do here) and no action on penalties for failure to report a theft of a gun, nor for the inadequate storage/protection of a gun (we have a LOT we could do here.)
But that's not what's being proposed. I'm fine with a heavy sentence for possession of a firearm by a prohibited person, assuming they clearly know they are prohibited. (Remember what happened recently with voting in Florida--the state told them they were legal to vote, then arrested them for voting. Set up a system that lets people know where they stand. (And I would make this more broad--if multiple interpretations of a law are possible the defendant gets to choose which applies. The law should not be a gotcha system!))
You aren't doing anything about illegal possession, just throwing roadblocks in the path of legal possession.
It's not difficult. If you haven't got a license, you're prohibited from driving, and you are reasonably expected to know it. If your vehicle isn't registered, you can't use it; And again, you are reasonably expected to know that too.
The same exact process can work in the same exact way for gun licenses.
Your desperation to make this seem impossible is noted and derided.