FWIW, you keep making sense, at least to me. Last year I think we can agree giving guys periodic rests, which runs completely counter to traditional views of what players should do during a 162 game season, sure didn't hurt and probably helped. It was the best season, especially the postseason, in Red Sox history, so the rest might have helped. So Cora tried to use rest for his starters in ST this year.
Plus, as you say, starters throw a lot of innings and pitches and one in particular, Sale, burned out in the 2017 and 2018 seasons. That's beyond question when you compare his April-July ERA's with his August-October ERA's. Another point in favor of extra rest for starters in ST.
That said, I do think April, for whatever reasons it went so badly, did create a confidence problem from which the Sox have not recovered. I suppose you can start with the rotation being so lousy in the early games, add in an 11 game west coast trip with no break which caused losses and overworked the bullpen, and suddenly the Sox are playing catch-up, the exact opposite of a year ago.
The 5 game winning streak ending May 12 should have created a burst of confidence, but since then the Sox have gone 7-10 since then and are in danger of going below .500 today. During that 7-10 run the Sox played 13 games without a break, including two starts (by Price and Velazquez) then last 2 outs and 1 out, respectively, which maybe why the bullpen collapsed vs. the Guardians.
Right now I think that Yankees bullpen is like the feather in Dumbo's trunk for the rest of the team--rotation and lineup--because they're thinking, "no biggie if we fall behind because the bullpen will shut them down and we can win later." Or, "all we need is a small lead that the bullpen can maintain forever." I say that because our rotation and hitting are about as good as the Yankees, but so far this season they are beating our brains out. Despite multiple injuries to their lineup and rotation.