If you really pay attention, it's not as brutal on the cast as you might think. Only a relatively small amount require the entire crew over an entire hour. Many crew members, even high level ones, have little or even no parts in many episodes, but occasionally they'll have an episode that focuses on their character, often in tandem with another character.

Theoretically, if there are 10-12 episodes that only include 2 or 3 characters for the most part, they can shoot many of them simultaneously, using different crews.

There might be a quick establishing scene here and there that requires other cast members (sending them on the away mission, in the transporter room, Picard barking orders, etc.), but the costumes and sets are fairly static on the ship, so if they have the scrips early, they could shoot a bunch of establishing scenes in a single day, and then edit them into the appropriate episodes.

Much of movie making is simply logistics.