Hold a gun to my head and I would guess that either Shatner was nursing an injury during Court Martial and Space Seed...or as said above, the director simply had other ideas and at the end of the day Shatner probably said, "What? I could have done all that!"
It's not like Shatner had no training. That wall-jump I mentioned earlier is something even I wouldn't have tried, and looks like it genuinely hurt.
What's funny about theatre stunt-fighting is if you do something too realistic and you'll take your audience right out of it.