That is an interesting scientific thought experiment, the Gorn ship got "crushed" because they wanted to give off old Submariner movie/show vibes ala Das Boot but I don't think thats exactly how gravity would work as you get closer and closer to a singularity - would it really "crush" stuff?
Spaghettification is definitely a thing as you get close due to tidal effects as Igarthy says (all points of your body would feel different levels of gravity pulling you apart), Neutron Star is a famous short story by Larry Niven dealing with the same thing. There's also inertial rotation, spin would create different effects as well especially as most black holes are spinning at insane speeds with high angular momentum so its possible different parts of your body could get flung around at different accelerations.
Don't really think its something to nitpick Star Trek over, what we saw is fine and really just a starting point to get young kids to be interested in the subject and do their own research, which is exactly what happened to me when I was growing up watching scifi.
ouch, wonder what happens to kids whose first exposure is Discovery or PIcard