It depends on the particular martial art. A lot of very famous martial art styles are purely performative, and are basically no use in any fight with a non-cooperative opponent or at least one not practicing the same restricted move set. Some of this was quickly demonstrated when a few famed practitioners made the mistake of participating in MMA tournaments. Some examples of such purely artisitic/ritualistic/sporty arts are sumo, aikido, capoeira, Krav Maga, and quite a few others.
Lyoto Machida uses Sumo as part of his MMA. At our school we've found it's pushing techniques useful once your get an opponent off balance.
The locks in Aikido are useful as pain compliance techniques used by people like law enforcement or bouncers. Compared to an art like Judo, the "throws" in Aikido generally don't throw your opponent to the ground and do damage. Instead they tend to cause your opponent to stumble away from you. Therefore, they aren't very useful in competition but they are useful in self defense where they can create an opening to get a weapon or escape.
