Your 'wager' is useless. You have absolutely no basis for your statement that private gun owners are more proficient with firearms than police other than your opinion.
What about incompetent firearms owners? There's tons of them. Should we give them a CCW permit too?
And FYI, knowing which end to point at the bad guy doesn't make you competent. There's a myriad of factors that need consideration when discharging a firearm in a crowded public location. "Bubba-Ray," who did a 1 hour course, online, is not competent enough with a firearm to safely use one in a crowded public place, IMO.
Sadly, people can get CCW permits with virtually zero training.