A case is nothing more than a box to hold all the parts in one place. Test benches don't usually even use a case. Pc repair shops have open air pc's, no case, toake changes or test other parts far simpler. There's many pc's that are part of furniture like desks and book cases or old stereo cabinets.
A pc case is on part of the pc thats honestly totally unnecessary, but is highly recommended since ppl have a need to transport, move, hide their components. As long as the dust is kept to a minimum, and you don't stick anything on the pc, like coke cans that are ½ full etc, there's no issue with it not being in a case as such.