Technically the only advantage is weight reduction. You still need a fork brace to help keep the fork tube parallel under stress and bumps. It is integral with the front fender.
Cosmetically, it is a fashion fad to remove fenders. Nothing says the owner is a master customizer better than demonstrating the ability to remove parts from a bike.

No fenders pretty much restricts actual operation to only fair whether days, unless the rider wears some sort of baggie style suits to ward off water, from rain, sprinklers, saliva, honey wagon spillage, road kill, and general road spooge, etc.
Nothing says seasoned cafe racer better than having a stripe of road grime running down your back or gritting between your teeth. Chicks love that, as well as the smells of having your nose an inch from any road surface debris imaginable.
All my bikes have fenders. And, the one I got with them stripped off I restored, as well as replacing the other dumb ass "racer-look alike mods" made to the bike.
Cheers,