Just my 2 cents
Unfortunately some martial art teachers only teach the striking component of the system and not the grappling component of the system and as a result the common assumption is that a specific martial art doesn't have grappling. Some think that BJJ, MMA, or some other grappling component needs to be included because the system lacks one. My theory is that all striking systems have a grappling component that was originally trained along with the striking, and that the grappling techniques that were developed allowed the practitioner to get the most out of their striking techniques used in their striking system. There's no way possible that humans can war against each other in ancient times without someone being taken to the ground. Even sword fighting had grappling techniques.
My Ignorant Statement: My theory is that early bare knuckle fighting included grappling techniques as well.
I think MMA just does what Modern Martial arts should have been doing, Teaching and using both the striking and grappling components of the system.
It could be that the creation of boxing as a sport is why some of the other martial arts ignored the grappling component. For a long time Boxing was big money and fame for fighting and all they do in boxing is punch. Maybe martial arts wanted to be rich and famous too so they focused on just the strikes similar to what boxing does. Now that MMA is a big money maker, people are going back to the grappling components within their system. In hopes to compete in a sport that is similar to MMA and get rich.
This is Korea's traditional grappling system SSireum
This is India's traditional grappling system Kushti.