Paul Molitor had something to do with Cooper's not playing. 1987 was the year Molitor had a 39 game hitting streak which began on the first day he returned from the DL. Trebelhorn installed Molitor as DH upon his return, replacing Cooper, who had been DH. Molly was comfortable at DH
and Coop never played again.
It probably didn't help that Cooper came out of spring training unable to play
until the 8th game of the season.
Of course, the Milwaukee press was asking questions
. Here's Trebelhorn's defense