my mosey around do nothing broodmare is barefoot. I ride her on the odd day, but she mostly is a pasture potato, and she enjoys it that way. She never needs her feet trimmed because she wears them down the way she wants them.
On the other hand
We have our racehorses. THEY have to wear shoes for a number of reasons
1- the biggest reason is the track. Without shoes they can't grip the track. The track can either be loose, hard, sloppy, etc. if they can't grip the track, they can't go. For an example, its going to be easier to sprint in running sneakers, than flat sandals because you can grip a lot easier with sneakers. Also we race in the winter. It can get very slick out there, so would you really want to be going fast on a slick surface with a barefoot horse? I wouldnt
2- hoof problems, brusing, quarter cracks, etc. a horse with quarter cracks NEEDS shoes.
3- gaiting. Sure horses can trot and pace without shoes, but when the speed is picked up, they can go from an awesome looking pacer, to a knee knocking mess. This is where corrective shoeing comes into play. You can shoe a horse to not crossfire, knee knock, etc. and this is key in racing. A horse that knocks knees is much slower than a horse who doesnt, and it causes them a lot of pain, and sometimes its so bad it can cost them their career.
Theres just a few reasons there, but there are a lot more.