I once had a guy on a plane spontaneously turn to me and say "You know, if you stopped biting your fingernails your hands would be really pretty." I do not bite my fingernails. I'm a cellist. And I do not recommend that as a pick-up line, in case you were thinking about it. This came back to mind as I was reading an offhand comment about needing to clip nails on Cellomania.
I remember how traumatic it was for girls to give up their fingernails in high school. Many didn't, and were stuck with a finger-slapping lousy-intonation no-vibrato technique. I'd bet they don't play anymore. Even if your technique leans toward using the fleshy part of the low fingertip to get a fat vibrato in lower positions, you need to get further up to play faster, and you can't play in thumb position at all if you're not up on those tips like a ballerina is up on her toes.
Since I started playing violin at age 10 I have had long nails twice. One summer in college, my string bass years, I decided not to practice at all and grew them. I had to cut them off when they got in the way of sailing. Slipping sheets + catching fingernails = ouch. And I grew them for six weeks before my wedding for the photos. That was during a long 15-year +/- stretch where I wasn't playing an instrument, but by then the short fingernails had become a well established habit. By the time I can see a fraction of a millimeter of white my nails feel too long.
My current teacher, T-, keeps nail clippers in his studio. I've seen him hand them to students during lessons with unspoken but specific instructions. My last teacher, T2-, told me once that when she writes her autobiography she has two titles in mind, and one of them was Life Without Fingernails. Yup. I know what she means.