I don't want them to have moments though, I want them to have episodes.
But why, though? Take Riker, for instance. He has very few episodes focused on himself but he became one of my favourite characters because he grew as part of the story and his interactions with the other members of the crew.
No, TOS definitely pulled off having a strong focus on three core characters. I've been watching it simultaneously with Enterprise and Discovery and I've never thought 'man I wish they'd give Sulu or Scotty something to do' like I did with Reed or Hoshi, or Detmer and Owosekun.
That's probably because ENT did like TNG and DS9 and made a point of introducing each character like they were important, only to focus on a few of them and give Hoshi and Mayweather the cold treatment. TOS didn't make the first mistake so it doesn't quite feel like a missed opportunity.