When you buy a whole fish of any decent size, the fishmonger will ask you if you want him to clean it up or gut it or whatever. The fact that he’ll do that instead of simply cleaning and gutting every time suggests there are circumstances where you might not want him to. My question is what are those circumstances? I know that when making fish stock for a bouillabaisse you sometimes use an entire fish if you are doing it the long-hand way, but that would be the exception as opposed to the rule (and even then it would only be some teeny-tiny fish that you wouldn’t expect to have cleaned up for you anyway).
Maybe one part of it is that opposed to some other food animals, cleaning a fish is relatively simple. Those who are fishermen that keep some of the catch can clean most fish with a few simple cuts and don’t mind doing so.
Does he get tips? If so, it appears like he is provididing more service if he cleans the fish in front of you - even if he would have to have done that anyway the other way around. Also it may save him a bit of work if some people don’t request it. Also it saves him the repetative work of precleaning them - as they are cleaned per order. Even if there is no tip, it does appear he is providing a higher level of service if done to request.
I you really seeing the ungutted fish on display? Unless they are pulled live from a tank I believe that they are gutted. I have been to markets where they will scale and remove the head of the fish if you ask.
I think it might also depend on the type of fish. Some fish, like trout can be prepaired with sometimes the head and usually the skin left on, they just need gutted and scaled. Other fish where one is only after the fillet need a bit more “cleaning” before they’re ready to eat.
I sometimes like to cook a whole fish on the barbecue. At other times I like to cut off the filets and broil them after sprinkling the de-scaled skin with salt, Japanese-style. In both instances, I will buy a fish that has been gutted and scaled but left otherwise left intact. I think western-style fishmongers who (at least in America) are only recently starting to carry whole-body fish again, they pre-gut the whole fish before putting it on display; in Asian markets, the whole-body fish is left ungutted and unscaled until you step up and tell the fishmonger just how you want it treated.
And yes, one also wants the fish frame, head and fins for a fish stock sometimes, so this is another instance when a whole-body fish is called for.