Although I have been out for about a year with a stubborn knee injury, I can still comment.
My style is Shotokan Karate. In that style punches, kicks, blocks and walking forward and backward occur, you need to do certain exercises to learn to punch harder (like punching pads and punch bags) and exercises not only to learn to kick harder, but also higher (achieved by kicking pads, punch bags and stretching).
I bought myself a leg stretcher and with this, combined with going to the gym regularly and losing weight, I have noticed my flexibility has benefited a great deal.
(Obviously, this also includes my karate practice sessions themselves).
I have now noticed that my kicks are going much higher than they used to, I can also stretch my legs much further than before (no stretches yet, though), and the warm-up, where you have to do certain warm-up exercises with crossed legs and reaching over to handle your feet, is now much smoother and easier than ever before.
However, having said all the above, you can also benefit from your karate practice alobe, provided you get rid of any excess weight and you do all the exercises truthfully and intensively.
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