Here's my :2cents:.
Fish has to strike a balance between flavor and texture. When the fish is alive, it's texture is fantastic, but the compounds that create flavor are locked up and working, doing their original jobs. If you are eating the belly, you are eating something that is anywhere from 20-60% fat, which does not perform a task, and it's flavor compounds are just stored up as available nutrients. As a fish degrades after death, more flavor busts out as the initial stage of decomposition, and it makes the flavor more accessible to your palate, but the texture suffers.
There is a traditional method in Japan of catching a tuna and burying it in the sand for 1-3 days before digging it up and eating it, for this reason.
Same principle as aging a steak I suppose.