Yes, but it needs to be done the right way so legit customers don't get rejected, and you can't do things like make everyone mail them a photo of their ID because they could sell that to a thief or credit card scammer. Or someone could break into their office and take it. Or they sell it and pretend it was stolen.
And when you start talking about regulation the two locksmiths will say the best way to do it is ban lockpicking tools so they can keep them away from other less ethical people, or ban other locksmiths coming from the next town over.
Continuing with your metaphor - sure get more security - you likely can never eliminate a threat. But if the bad actors are reigned in at a systemic level, you can get away with a lock on your window instead of steel bars.
I'm of a view that in a society we are better off when we all can get away with lighter individual protections as otherwise, thos who cannot afford the necessary security end up suffering.