The Ultimate Computer was really the first episode of Trek to show us that Kirk wasn't really needed on many of the away teams! You need a medical officer, but it didn't have to be McCoy, a science officer and that didn't need to be Spock and a chief geologist that didn't need to be D'Amato!

TNG had this type of thing with Picard rarely going down to any unknown planets or even known ones and leaving it all to his team of experts instead! Kirk just had a taste for the action and he wanted his mates with him!
JB