I think what You guy's are discussing are two different things actually, but close, very close.
The breaker is always meant to Function, It should always trip when a load is put on it that exceeds the breaker rating for a certain amount of time. When it is underrated for the wire it becomes a nuisance breaker cause it always trips. Is it code is another story.
We can have an underrated breaker on an air conditioner condensing unit because the unit only uses more power on start up. Say It is rated at 38 amps and it is installed on a 30 amp breaker. This is for start up only and is only a couple of seconds at most. Then the unit continues to run at a lower rating than the breaker and does not trip.
When you connect a small wire to a larger wire in the panel to accommodate the breaker hold down or lug, it has to be in the panel and a certain size and length. This is allowable as far as I know.
I have seen with my own peepers where a breaker does not trip and starts to smoke. It was the correct wiring and not a different company breaker. Me thinks it went bad.
So as far as not functioning that would go in this area of the conversation.
What Square Eye is saying is that HIS inspector such as county or town says no. He can do that because he is in charge....even Petey has to do what he wants him to if he works in that town.
I have seen many strange things in a panel. The reason we inspectors call things out is to cover our assets we work hard for. I let the pro come out that is licenced in their area of expertise. This may cause some inconvenience but it is safer in the long run, and the pro will probably get some legitimate work out of it. No harm done.
Is it done to manufacturers instructions is another.
Now about those Federal Pacific panels...........