After way too much pondering on this subject, I think the bench coach does matter relative to the manager, as much as the manager. I think Tingler was a bad fit for Baldelli because neither were in-game tacticians. If neither your bench coach or your manager are tacticians, then you will get regularly outmaneuvered by the opposing team who will have a tactician on the bench.
by my little bit of research into Shelty, it was Molitor who was the tactician and Shelty the big picture guy (though his rep as far as I can tell is more tactically capable than Baldelli). That might make a Tingler type bench coach a bad fit for Shelton.
Hopefully the next bench coach is a better complement to Shelton such as a coordinator/chess player type to make sure Shelton doesn’t paint himself into the platoon corner as Rocco did night after night.