The actor's salaries are also usually less in the early seasons, and it's well documented how Shatner and Nimoy negotiated their way into better deals each passing year of TOS.
Actually my understanding is that actors get raises every season, which is one of the factors that make shows more expensive over time and lead to cuts in other areas. This is why so many long-running shows let cast members go and bring in new ones. By season 10 of
Smallville, for instance, they only had four regulars, only one of whom (Tom Welling) had been a regular from the beginning.
Law and Order also periodically replaced its leads, and the
CSI shows have rotated out a lot of their cast members over the years; the flagship show is now on its third lead actor. And the
Power Rangers franchise has survived for 20 years by bringing in an entirely new cast of (non-union) actors every single season (or at least every second season).
So there's every chance that a fourth season, with increasing actor costs and a decreasing budget, would have simply followed the trend set in the third season. I barely wont mentioning it, but it's even entirely possible that some of the supporting cast would have to be shed to get things back on an even keel (show's are certainly not adverse to taking these measures). Shatner, Nimoy and Kelley were more or less the only 'esssentials', so it's possible Freiberger or whoever else succeeded him would look at the supporting cast and say "Sorry Nichelle/Walter/Jimmy/George, but your services are no longer requested". The Enterprise could be staffed by day-players if necessary for a fraction the cost.
Again, the animated series is worth considering as a genuine continuation of
Star Trek, because what we're talking about did essentially happen there. Originally, Filmation didn't even intend to bring back Nichols, Takei, and Koenig, presumably intending to have their characters doubled by Barrett and Doohan or perhaps by less expensive voice actors (similarly to how Jane Webb played both Ginger and Mary Ann on
The New Adventures of Gilligan). Nimoy convinced them that excluding both minority cast members would be a really bad move, so they paid the extra money to hire Nichols and Takei (which proved invaluable since they both played so many guest characters), but they still didn't have the money to bring back Koenig.
As for Freiberger, it might be worth looking at how he handled
Space: 1999 when he took it over. In the first season, S99 had an ensemble not dissimilar to
Star Trek's: a core triumvirate including a commander, science officer, and doctor (John Koenig, Victor Bergman, Helena Russell), a group of four supporting players including one black actor and one Asian actor (Alan Carter, Paul Morrow, Sandra Benes, David Kano), plus a secondary medical officer in an occasionally recurring role (Bob Mathias). Although S99 arguably did a better job fleshing out this supporting ensemble than Trek did with its ensemble, giving them nice character moments here and there and occasionally showing a developing romance between Paul and Sandra. But for season 2, Freiberger felt that the supporting cast was rather bland and he intended to replace all of them, but he was convinced to keep Alan and Sandra due to their popularity with the fans. But Bergman was replaced with the sexier Maya, Paul and David were dumped, Alan was overshadowed by the new "security chief" Tony Verdeschi (who did all sorts of things that had nothing to do with security), and Sandra was reduced to more of a bit player and replaced in a number of episodes by one of two other minority actresses (and even had her name inexplicably changed to "Sahn" in the latter half-season). Bob Mathias showed up in the first part of the season but was then replaced by another black male doctor who was in turn replaced by yet another black male doctor, treated interchangeably.
Nimoy was under contract, so I doubt he would have walked. Not that actors didn't break contracts from time to time -- Barbara Bain walked after three seasons of Mission: Impossible in 1969 -- but I think Nimoy was smart enough that he would have stuck it out rather than break his contract and risk his future career.
Oh, hadn't realized that.
So a Freiberger-run fourth season might have focused more tightly on Kirk, Spock, McCoy, and Scotty, and probably Chekov since he was popular with the girls, but Sulu and Uhura might have made only occasional appearances or been substituted with other minor players, possibly of the same gender and ethnicity.
