Francona remembered when he was coming up, before Automatic Eck in the 9th started a trend and then Rivera set a longevity standard that no one else could ever match -- but every team always had to try and contrive. Before the 1980s, the best relievers always threw multiple innings and came in a lot sooner rather later. Sparky Lyle, AL saves leader in '76, entered an elimination game the next year in the 4th inning and pitched the final 5.1 for the win.
Also, recall Cora tried this the first half of '19 - calling on Barnes in only high leverage match-ups, usually before the 9th. It worked for awhile, then Barnes got burnt out, possibly from overstressing his arm and his brain.