The total absence of a main character from an episode does raise questions. I mean, a ship's doctor might remain unseen, but McCoy is such a busybody; a chief engineer might be off camera if all went well, but no episode is based on all going well. If these people are absent without explanation and 1:1 replacement, something is lacking.
The secondary bridge heroes have every excuse of being rotated off duty, of course. The odd thing about that is why the sidekicks are so seldom replaced by corresponding other officers; it almost appears as if they are the "A Team", the shift that is awakened every time an adventure is anticipated, and then stays on duty until the credits roll. But there are adventures that start in the middle of the teaser, not prior to it, and nevertheless the "A Team" already occupies the usual consoles...
In TNG, we often had main characters leave the ship and attend various meetings, conferences, competitions, holidays or whatnot. In TOS, nothing of the sort was ever hinted at; shore leaves were rare occasions that impacted on the entire ship, and no courier service could whisk people off the ship for the duration of a single episode (or else there would have been no "Amok Time").
So... Where is Scotty?
They may not have taken the effort to explain it in-continuity on TOS, but on this type of show, it seems to be pretty standard for most of the actors to get at least a couple of episodes off per season. On TNG, IIRC, everyone but Stewart and Frakes was routinely missing for two or three episodes a season.
And on TOS, Scotty and company weren't even regulars listed in the opening credits...they were just recurring guest stars listed in the end credits.