We can see that now, because we have big-screen TVs and HD-quality home video. Audiences in the 1960s were watching on smaller sets, often in black and white, often with much less image clarity, often through fuzz and distortion due to poor signal reception or mis-adjusted knobs. (There were so many things that had to be synchronized or tuned just right to get a good picture, and they all depended on manual adjustment. You often had to work to get a decent picture, and sometimes "decent" was the best you could hope for.) So the substitution of the stuntman for the actor wouldn't have been nearly as obvious at the time -- which was why they were okay with doing it that way.
Trust me; this is exactly correct. As one who has watched TOS from the beginning. I never noticed the difference simply because you couldn't tell back then with the primitive equipment.
Yep. The fight scenes in Space Seed and Court Martial never looked bad to me on a 19-inch CRT. Then I got my 32-inch flat screen and it was pretty obvious.
Nimoy's double stands out a bit in Mirror Mirror, in the Sickbay fight
So does Uhura's stunt double stand out a bit in "Mirror, Mirror", in the Sickbay fight scene now, but not back in the 1960s as others have said. Here
is a hd picture of her stunt double, you can see the rolls of fat on the stunt double that actress Nichelle Nichols did not have.
Navigator NCC-2120 USS Entente
Stokely: In an insane society, the sane man must appear insane.
Harvey Holroyd: Where'd you get that?
Stokely: Star Trek. [leaves the room]
Harvey Holroyd: [to himself] God, I miss that show. (Source: "Serial", 1980.