The first season of TOS had an episode, "Shore Leave," where the Enterprise makes a stop over at a planet for the sole purpose of wasting time and relaxing.
I think you're right, though. It's not so much that there's no time wasting, but the show was about the adventures of the Enterprise and its crew. For all we know the crew in TOS spent 99% of the time screwing around, and the show was about the 1% of the time they spent working.
The only reason "Shore Leave" was even an episode is because something went very awry on the shore leave planet and action and adventure ensued!
Which goes to show--really, the reason they don't show anyone goofing off on Star Trek is because goofing off isn't very entertaining to watch and because it's an action-adventure show about action and adventure, and not a show about people's everyday lives. At least by DS9 they realized it would be entertaining to show the crew trying to get into each other's pants.
It's like James Bond. You see in the movies the one week every couple of years where he's actually being a spy. The rest of the time he sits at a desk at MI6 HQ doing paperwork.
I think you're right, though. It's not so much that there's no time wasting, but the show was about the adventures of the Enterprise and its crew. For all we know the crew in TOS spent 99% of the time screwing around, and the show was about the 1% of the time they spent working.