What are the standard reasons given in favour of having a higher bar to concealed carry (requiring more certification or more stringent background checks)? I would guess that some percentage of people out there (myself included) would be potentially uncomfortable interacting with anyone who has a firearm, and certainly would want that information to be available to make an informed decision.
There seem to be two models of crime, and the differences drive a lot of the politics here.
Very Bad Day Model: Violent crime happens when stress, tragedy, or other factors push someone over the edge. Then they commit violence with whatever is at hands.
And:
Career Criminal Model: Violent crime happens when a serial predator makes a mostly-premeditated decision to go looking for victims.
Progressives tend to think in terms of the first model, and imagine a scenario where some previously-law-abiding guy gets cut off in traffic and goes all road rage as a result.
This (IMO) drives a lot of requests for training. No one really cares if gun owners know how to properly clean their guns. No one really cares if they can reload quickly, or shoot a 2 inch pattern instead of a 4 inch pattern at 20 yards.
Instead, the hope is that spending N hours considering the implications of force will make people less likely to make a tragic and horrible decision in the heat of the moment.
This model also justifies a desire to know. If any of my coworkers could snap, given a bad enough day, then their carrying presents a real risk to me. And a carry ban represents a meaningful improvement in my safety, since it means they'll be unarmed when they commit violence.
Conservatives tend to think in terms of the Career Criminal model. To them, public violence is committed by a small population of bad guys. Training requirements don't matter, since the bad guys won't pass even trivial hurdles like "show up, let the cops have your fingerprints and pay $50 for a license."
To people who think in terms of the Career Criminal model, worries like "That 45-year-old dentist has a concealed pistol! He could shoot me at any time!" are basically unreasonable. Obviously, people are still entitled to feel their feelings, but reasonableness matters when the fearful person is asking everyone else to change their behavior.