Perhaps not you (since I don't know your background), but in general do you feel training makes no difference?
Would you say a heart surgeon with decades of experience would be arrogant to say they are a better heart surgeon than Joe Blow on the street who has zero medical experience? No, they truly are better, because their education and experience.
So yes, people can train to become far better drivers than the average. Hardly anyone does, because it is not required and most people don't care. But it is very much possible.
I think training could help. However I don't think it will. People think they are good enough and will write down answers to pass the test. Maybe if the training was mandatory behind the wheel with failure meaning you lose your license - but the voters won't stand for that.
Are they struggling with a 4 way stop - or did they just prevent a crash because someone else you didn't even notice just did something stupid? That someone else might be you not knowing you even did something wrong!
Of course I have no idea how you drive, how much training you have or the other important details. The above shouldn't be taken as a personal attack on your actual driving. The attack does fit every other driver I know though (including me - though it is hard to be honest about my own failings)