With "Space Seed" (no current copy unfortunately), one thing that hurts the fight scene is the stuntmen are visible far too long and there's not enough intercutting of close shots on Shatner and Montalban. Maybe there wasn't enough time to shoot the additional angles.
The most dangerous stunt looks like where Kirk grabs the grating in front of the forced-perspective set, and doesn't he wrap his legs around Khan? I can understand why they might not let the stars do that. There's risk of injury to the other actor, and if that grill wasn't secured properly, the whole thing could have fallen out.
And even a simple stunt like a fall, or struggling, could cause a pulled muscle or sprain sidelining an actor. On The Wild Wild West, Robert Conrad often did his own stunts, and once cracked his head open when a chandelier swing failed and the prop crashed to the floor.