I did it a few times in high
I did it a few times in high school for big swim meets and my opinion hasn't changed. I think shaving down is 98% mental. If this were a 50 or 100m sprint then the drag caused by the hair might have some effect, when the race is down to tenths of a second. But in a 2:30 race, no, it doesn't make you physically faster. Cyclists shave down too and their reasons are that when/if you crash gravel doesn't get caught in the hair and make it worse. Also because it makes the post-race massage easier.
But in my opinion a massive part of racing is mental. And shaving down is one of those things you can do that makes the race special and different and real. It's a way of telling your mind and body, "Ok, this is a serious thing. We are taking extra steps to be as prepared as possible." For me, it helped get my head in the game the day before the big event. So The Itch now is worth it.
...and my legs are damned sexy.