Partially true, but I'm 99% sure the main nozzle check valve in a butterfly carb is crucial for a stable idle.
Either way a faulty main valve will allow the purge bulb to suck air through the nozzle rather than fuel from the tank.
And yes you can check a mechanical main valve with a piece of hose. Not so with a screen valve, these really can't go wrong other than plugging up which would cause other problems.
Of course you could stop fiddling and get a new carb .
Then working off that theory, a float feed carb would need a check valve also, wouldn't it?. There is no fuel being pulled off the main when the throttle plate is closed, so there is no need to shut it off. AND, there are check valves in the primer flange also, which don't affect running but will affect primer operation. I definitely agree with just replacing the carb. Replacing the check valves in the body can be done and the repair will work if in fact that is all that is wrong with that carb.
It's not worth the time in a repair shop environment, and I wouldn't waste my personal time (unless the repair got "personal')