The problem is that the "compromise" touted by gun control advocates is entirely one-sided - more restrictions, no concessions. No quid-pro-quo, only further restrictions on the right.
What concessions would gun rights advocates accept in order to allow some restrictions? What's there left to give on this issue that wouldn't undermine any controls.
Say, for example, I wanted gun owners/users to be required to be as responsible as car users, i.e. pass a test, maintain a license and registration for weapons and weapon users, and hold liability insurance to cover damage either intentional or accidental (that would obviously scale with the likelihood and amount of damage the gun can do). What can gun control advocates give that will get that done?
I think part of the reason the gun debate can be one sided from the "control" side is that the US already is quite far to the "rights" side of the spectrum, relative to the rest of the developed world. It can be difficult to see where we could plausibly move further in that direction without causing more of the problems we're (hopefully) all trying to solve: unnecessary bloodshed.
In your example, since we now have a mandatory testing/licensing scheme and insurance, I see no reason why CCW's countrywide shouldn't become shall-issue. There should also be a stipulation that licensing is a thing you grant to people, not individual weapons.
Another example I floated in previous threads is surfacing psychological issues in NICS checks (stuff like certain diseases or involuntary holds) and granting access to that system to everyday people rather than just retailers.
That's not compromise, that's capitulation.