I think this is a mistake on a statutory and common-sense level.
Legally, carrying a firearm introduces a trove of civil and criminal liability issues. This language governing CCW is cryptic and spread out over a lot of laws; a course consolidates this neatly for people and ensures they understand it. It's going to be difficult for even well-meaning people to do this on their own, and then there are just the irresponsible people who don't care. We'll be seeing a lot more firearms on crowded metros, buses, in bars and other places where they can't be used without wounding/killing bystanders or just shouldn't sensibly be.
Practically, the course also provides a lot of information about safe gun usage, maintenance and storage -- habits which, in my experience, at least 30% of people do not regularly exercise.
My thoughts on the machismo present in broader American gun culture at large notwithstanding, I think these courses did a great job of reminding people that guns are dangerous tools that must be treated with care and used only as a weapon only as last resort. People are apt to forget that when they put one on their hip, and I think abolishing the training will probably have some repercussions (not massive, but tangible).