Pellegrini has made other questionable decisions in his brief tenure at the helm.
He has stubbornly relied on midfielder Javi Garcia to fill in at centre-back in Vincent Kompany's absence. He turned away from his purported "main striker of the team," Edin Dzeko, after 140 minutes of Premier League football.
But squad rotation is unavoidable for a manager competing in, at present, three tournaments and a league title race.
Changing keepers, though, is the sort of risky proposition normally left to sides residing in the bottom half of the Premier League table. As the old saying goes, if you have two keepers, you really don't even have one.
Perhaps Hart forced Pellegrini's hand with a series of high-profile, low-return errors. And things were going swimmingly with Costel Pantilimon in net, at least until he gave Phil Bardsley half an acre to shoot at in City's 1-0 loss at Sunderland.
The merits of the keeper change are not worth revisiting. Pantilimon is City's keeper in Premier League matches and in Champions League play until further notice.
It is that "further notice" part, though, that Pellegrini screwed up.
Pellegrini's unwillingness to come down hard on Hart is doing Manchester City more harm than it is doing Hart good.
Pellegrini was recently quoted thus by Chris Richards of The Mirror: "For the moment we are playing with Pantilimon but we are all supporting Joe Hart and he will come back, but I can't say when."
That flippy-floppy quote is right in line with the Mike Whalley report on ESPNFC.com which had Pellegrini saying this: "And at this moment, I repeat, I will trust in Pantilimon. But we continue to trust in Joe, and we will see when he can come back."
By these words, Pellegrini has taken all of the threat and all of the sting out of Hart's demotion—and all of the certainty out of the keeper position for the field players.
No one is served by Pellegrini's soft stance.
Hart cannot possibly be properly motivated to put in the work on the practice pitch and in film study that he needs to to get his job back, since he knows he's probably getting it back soon anyway.
Pantilimon has been labelled a place-holder through no fault of his own.
And both keepers and all the field players must deal with ongoing, annoying questions about whether their first-team keeper is Pantilimon, Hart or maybe even someone else.
Has Pellegrini handled his keeper situation properly in the aftermath of demoting Joe Hart?
Once he pulled the plug on Hart, the smartest thing Pellegrini could have said about the switch was nothing at all.
Instead, the manager has plunged his side, the deposed star keeper and the stopgap into needless turmoil.
Whenever Hart gets his job back—and Pellegrini has made it pretty clear that he considers it Hart's job—he had better play consistently great football from the first moment of the first match.
For his own sake and for the sake of the manager who expressed gratuitous faith in him to the detriment of all concerned.