The problem with most (if not all) case gauges is that they only check the brass dimensions, they don't simulate the throat/leade of the actual chamber. In other words, you can't plunk test your ammo in a case gauge, you must use the gun's chamber to do that. Even the case gauges that advertise they are made with actual SAAMI reamers may not (and probably won't) match the chamber in YOUR gun.
The problem with chambers is that they are always looser than SAAMI specs, but one gun might be looser than another. If you use a case gauge to check your ammo, you at least know that the brass part of the cartridge will fit any gun's chamber.
Whenever I get a new bullet to try out, the first thing I do is to plunk test it to determine how deep I have to seat that bullet for it to work in all my guns. If I check the COL of my loaded rounds, and run them through the case gauge after they are loaded, I know with reasonable certainty that they will all chamber and operate in my guns.