The mixed martial arts organizations disallowing it usually do so because elbowing the head increases the risk of lacerations in a fight.
Some well known and respected traditional martial arts that use elbows are Karate, Hung Ga, Bajiquan, Wing Chun, Silat, Lethwei and Muay boran.
The hardness of the elbow allows for hitting with considerable force, and experienced fighters can easily knock out, cut, or injure their opponent with a well-placed strike.
Elbows are generally most effective when used in combination with punches or kicks to allow the fighter to close the distance.
It is not recommended to strike solid objects for conditioning as micro-fractures in bone or other tissue tend to be a risk factor for repetitive strains or even more acute problems.