that.... actually looks like it would be extremely unpleasant. I imagine gills would be very easy to bruise
The actual soft gas-exchange tissue might be. Which is why it's protected by gill arches and operculum (gill covers, the flaps on the outside) - reminder that they're openings on the sides of the throat where food passes through too, and for many fish "food" equates whole other fish.
Evolution handled such details long ago.
Just to nerd excessively over the anatomy, though, it doesn't really make much sense for the gills to be located there. When you get down to it land-vertebrate lungs are ultimately derived from the swim bladders of the ancient bony fish that started experimenting with this "dry-land" business all those millions of years ago, and several extant fish species today use theirs primarily as a lung analog too (for example to survive getting trapped in isolated oxygen-poor pools after rainy seasons).
Cartilaginous fish - sharks, rays etc.- don't have swim bladders in the first place making this interpretation doubly dodgy.