Yup. Good point. Since the ship I served on was built in the 1940s, it was geared towards subs that had less diving depths... about 850 feet. I took the 800-foot plunge in that SRC... THAT was a blast...
So, since we weren't really needed for sub rescue (though we did drill and drill and drill...) we spent our time doing dive ops, torpedo recovery, Trident II missle launch security... ya know, the usual ;0)
The fact you never had to make a sub rescue says volumes!
Besides none of us really wanted to do the things we drilled the most on. Though launching a couple 48's at an enemy sub would have felt gratifying...... as long as we hit and they missed.