His best performance in a game against a tough opposition this season for me was Villarreal Away (okay, they're not quite Liverpool, but they're last season's Europa League winner and this season's CL semi-finalist), where Carrick benched him for Donny. He came on for the last 25 minutes, didn't misplace any Hollywood balls, dictated the play & completely changed the game: we pretty much dominated Villarreal from the minute he came on. He himself had a great assist for Sancho and could have had two more if his teammates didn't miss relatively easy chances. According to WhoScored, his passing success rate in that game was 87%, whereas his average for this season is only 77% He also made more key passes in just 25 minutes in that game than on average per 90 this season. His body language that night was moody as hell though, had no reaction at all when Sancho scored.
I'm not calling Carrick a world-class man manager or anything like that, but maybe Bruno is someone who would benefit from being benched once in a while (i.e. not feeling that he's undroppable) to stay focused and actually play to the manager's instructions and not try killer balls every time.
I remember after the final whistle in the Arsenal game (where he had another good game and ended a goal drought), he embraced Carrick and whispered into his ear for a long time. It was probably just him being emotional that Carrick was leaving, but maybe he was finally admitting that being benched helped him?
Carrick in his final post-match press conference that night also joked about how Bruno was moaning all week about being benched (youtube.com/watch?v=Te4z66cR2CA - at around minute 4:50). At the time I didn't think much of it, but when you actually think about it objectively, that's really quite unprofessional behavior from a player (A key player moaning about being benched all week on the training ground can't be good for the team's morale) and it definitely fits Bruno's petulant character. Maybe Ole and Rangnick saw this kind of behavior too and was scared to bench or even rest him even for a single game, even when such a kick in the ass was probably needed to revert a run of bad form. Carrick, being the only manager with nothing to lose anyway, actually did what was needed and got the best out of him for a while.