well, to be fair, his era problems are mostly due to 2 cruddy appearances - 4/4 Rays and 5/6 @ AZ. he's given up 1 earned run over 18 appearances since, and his walk and k rate since 4/7 is in his career range.
https://www.fangraphs.com/players/kyle-finnegan/15009/game-log?position=P&season=&gds=2023-04-07&gde=2023-05-25&type=0
He's has a 4.25 ERA over the 9th inning in his career. Comparing him to Josh Hader is laughable. One is elite. The other isnt even good. FInnegan has a 5.53 FIP and 5.83 XERA. If anything, Finnegan has gotten absurdly lucky this season.
Again, the season is not about winning, its about developing. The only reason Finnegan should be given any closing chances is to build trade value.