Honestly, kicks are more of a range modifier to me, not a damage difference.
Shadowrun had a pretty good reach system for melee. If your melee implement (including kicks) had a longer effective range than your opponent's, you could leverage that standoff distance as an offensive or defensive modifier.
If you combine some kind of system like that with a constriction factor, I think you would have a really solid basis for the basic striking system. A sword is great in the middle of a field, but if you're in a narrow hallway, a knife will probably be more practical.
Start there, then you can potentially start adding to the grappling system.
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