Carrots often have dirt caked on the outside that's hard to get off with just water, so peeling is a good way to help with that.
The peel has the healthy bits
Sort of, but not really. The nutrients of a carrot may be slightly more concentrated in the skin, but all layers of a carrot contain those nutrients. You're not depriving yourself of an appreciable amount of nutrients by peeling a carrot.
https://www.allrecipes.com/article/should-you-peel-carrots/
Carrots are not like other vegetables