In fact, it is fairly easy to lock up the rear wheel and make it skid, unless you are running a rather high gear. Some fixed-gear fans make a point of not using their brake except in an emergency. I am not sure that this is a good idea. Heavy duty resisting is widely reputed to be bad for your legs, and to be counterproductive for building up muscles and coordination for forward pedaling. This is a lot like car drivers who use their transmission and clutch to slow down, even though the car has a special set of parts made for the exact purpose of slowing down.
Brake shoes are cheaper to replace when they wear out than clutches are.
Pedal Strike t is never a good thing to strike your pedal on the ground while cornering tightly. On a freewheel bike, you can coast though the corners with your pedals horizontal, thus avoiding any chance of striking. On a fixed-gear machine, you don't have this option. If you do bang a pedal on a fixed gear, the pedal can lift the rear wheel off the road, and down you will go. This has never happened to me, but it is something to bear in mind.