I wear a helmet at home when I'm training. It's not compulsory, but I do "just because". I know a few people who also train at home every day in a helmet, however have sustained some life altering injuries. One woman I know broke her neck. So I don't expect to be excluded from all injuries, as no one should. The second you are on the driveway to the barn, your chances of injury compared to a "normal" person go up at least ten fold. Such is the nature of dealing with a wild animal ten times your own weight. The same way cat owners are more susceptible to being scratched.
I really think that helmets don't serve to protect people as well as everyone might think. Nor to back protectors. Many people think if they wear these devices they become somehow more safe and do things they wouldn't otherwise. Infact, especially after being involved in vaulting, I am more and more of the belief that these safety devices serve to unbalance the rider and make them more prone to a fall of they are not used to the equipment. The most important thing we can teach our riders is how to fall and this - not my helmet - is what has saved me from any catastophic injuries in the past decade.
Education is what prevents injury. Education on how to fall, education on your limits as a rider, education on correct conditioning and maintenance of the horse, education on basic riding skills and equipment adjustment.
Having a basic liscencing program for equestrians would greatly mitigate the risks associated with horses. As well encouraging helmet use, yes, but driving down a highway going 100mph without a liscence with your seat belt on does not make you "safe".
As far as in competitions - again for those in flat work disciplines over the age of 18, it should remain a personal choice if one should wear a helmet. I feel like with correct education, people should be able to make their own informed choices. I for one am not about to ride a 4 y/o in his first show with a top hat.