I also carry a knife. Normally for non verty issues or rescue, BUT while there are *usually* other options, they may be technically difficult for some or take too much time. I also suspect that if you caved yourself into a situation where you think you need a knife then you might not be capable of caving yourself out of it without one
Consider an instance where 2 ropes were rigged near each other (yes a bad idea) get tangled, and a caver rappelling down from above the tangle can't or won't changeover and/or is in water spray. Certainly there are things to consider and precautions to take, but I think it might be easier and ultimately safer, to cut the spare (not in use!) rope and let it fall away (assuming no rebelays as is normal in much U.S. caving) than have them try to untangle the rope or do a changeover they aren't comfortable with while getting drenched on rope.
Another situation that caused me to nearly use my knife in a vert situation: I was ascending up a pit and there was a very narrow constriction near the entrance. I had enough *insulation*
that I really had to fight my up the slot..mostly inchworming with friction rather than actually ascending. my footloop had slipped off (I dont use chicken loops) and eventually snagged a flute. I couldn't get down to it to free it, and I couldn't fit past my handled ascender, or undo the screwlink attaching the loop to the ascender by hand. (too tight). I *could* reach my knife, and could have cut my loop free, then ascended using my croll and pantain for the remaining 8' of pit with my handled ascender/cowstail pushed ahead of me. What ended up happening was I got the loop free by brute force (I might have actually broke the flute?) I could also have had another caver climb up below me. But I very nearly used my knife then...and yes I wasn't about to cut towards me OR the mainline.