As a martial art that for the most part focuses on kicking it shouldn't be a surprise that it's that effective.
Bruce Lee's introduction to kicks, I'd assume, was Wing Chun. Most people seem to forget or ignore that Wing Chun has basic kicks too, even though it's true of course that the main focus is on the punches. Having had that basic introduction to kicks however wasn't unimportant, it opened up a path.
I'm not sure what he has trained inbetween to further develop his kicks, but it's known that at some point he has started training with TKD grandmaster Jhoon Goo Rhee. Bruce helped him with non-telegraphic punches while he in return helped Bruce perfect his kicks, especially the side kick.
TKD has probably the best side kick, kind of how Muay Thai has the best leg kicks. And you're right about the footwork, it's good. I'd compare it to Stephen Thompson's karate footwork, it's pretty similar.
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