That has been covered multiple times - in the parlance of the 1780's, well regulated meant functioning properly, not controlled by the state. Quick Karl may not like it, but that has been the conclusion of historical scholars and the Supreme Court.
Meanwhile, dspieler, anybody who carries in public already is held accountable for what he does. Whether he realizes that or not, it is true.
The problem with mandating training, is that anti-gun governments could simply create onerous training requirements. For example, see Chicago's initial responses to the striking of their gun ban - a firearm purchase applicant would be required to get training and certification, but Chicago would not allow training ranges to open in the city.
In some instances, people don't have money for a class. In some, they can't get transportation. In some, they lack the spare time.
Please note that ALL those arguments were used in multiple states this last election cycle, and by the US Department of Justice, to fight against movements to require photo ID's and proof of US citizenships for voters...