From a storytelling standpoint, later series had the holodecks. So they could do "time travel" episodes anytime they wanted, without the slingshot.
Yeah, watching some of these old episodes makes me wish that they had better back lots when they were originally filming Trek. It's too bad they didn't have a Kubrick or Ridley Scott set to hijack every once in a while. Instead it was, "Ah yes, we're stuck in the old west... ...again."