I think you have it. Ideally, a good bullpen can "lock down" the 7th, 8th, and 9th innings, which means facing every hitter on the opposing team. So that good bullpen should probably have several pitchers who, if asked, could close because they are that good.
For those who believe the closer is the key to winning, please don't forget Craig Kimbrel, the Sox great closer who wasn't so great, at least not in the 2018 postseason when his ERA blew up to 5.91.
In game 1 vs. the Yankees, Kimbrel gave up 1 run to make the score 5-4, and got a save. In game 4 vs the Yankees, he gave up 2 runs and got another save. His 3d postseason save, vs. Houston, was again after giving up a run--the Sox won 7-5. Another run, another save in an 8-6 win over the Astros. Finally, his 5th save--again vs. the Astros--included no runs score and a final score of 4-1--and in his 6th save vs. the Dodgers, he again gave up no runs in a 4-2 win.
In the 2018 postseason, the ace reliever for the Sox was beyond question Joe Kelly, who gave up 1 run in 11.1 innings. Eovaldi was also magnificent in relief. Barnes went 8.2 innings--against three really good hitting teams--giving up 1 run, and so did Brasier.
So, all in all, I think the mystique about the necessity of THE GREAT CLOSER is mostly a bunch of hooey.