I studied savate (French kickboxing) for a while, as well as some karate. The savate really did wonders for my flexibility and balance in a way that I didn't experience with the karate, and it also felt more applicable in the "real world" in the same way that krav maga and other close quarter / street fighting martial arts do.

To echo @TexMexBazooka, the real lessons were in de-escalation and knowing how to defend yourself decisively to enable escape from the fight. My savate instructor was very clear that any and every fight was a deadly one and that if he found out we fought instead of escaping he'd kick the crap out of us and then kick us out of the program.

I think there's also a benefit in learning how to take a hit, even though the goal is to avoid those. There are lots of body mechanics involved in fighting motions and practical experience taking and avoiding hits teaches you to recognize those movements automatically.