I'm just playing Devil's advocate here, not trying to instigate. But there is always a chance of something happening.
If I did make a mistake they still have no reason to search me or my vehicle. Yes, I'll take that chance.
God forbid you have an accident, or, they don't need to search you- only to ask if you have any weapons. Are you prepared to lie if you are asked that question? What if after that, for whatever reason, they do find out you lied?
I can't accept breaking the law, not matter how good the intention is. If that means I must ride with the gun stowed and unloaded, that's what I'll do. I will hate doing it, but I won't break the law and risk that type of trouble.