It can be both, one situation to the next.
You can only make a FOIA request to the US government.
I should think it obvious that yes, every department should in fact be staffed to a level that allows them to comply with this (and all other) legal obligations. Doing otherwise is obviously malicious.
This law was passed last century, back in 1966. It's not like this is some surprising new obligation that they failed to staff against.
Like, technically these requests cost nothing, because they pass the costs on - and because in this case, they've presented an absurd cost to avoid having to do anything at all