He was appointed as an interim to get results and I am judging based on that. Look he may very well take out the weed and in 2 years time he could be the best thing that happened to this club but as a manager I don't think he was a smart choice. I know hindsight is funny but I would rather had Carrick as an interim with Rangnick starting his consultancy role right away.
Unless you appoint a new permanent managerthen , and start the rebuild with January window; interim manager more often than not is a mean to damage control, and make space to distance a the failing regime from the next permanent appointment. Turning down Conte, there was no really a permanent option for us to go at the time.
Carrick is way too closely tied with Ole regime, to take interim and really be truly professional about interim job as his own boss. Put it this way: If thing turns out exactly like under RR for Carrick, Carrick would be in awkward position where he can't speak out about how thing done wrong under Ole. It can be seen as back stabbing, yet truth need to be told.
He had some positive result, but the football is not exactly positive. There was a lot of changes between and during in those games Carrick managed. It seems like even him staying with the team for all this time, he himself has no solution for this mess. We never know if he would do better in a longer run. However we know Carrick only option would be doing better and seriously get result, or it would damage his own future coaching career. IMO, Carrick is smart enough to quit from this political mess.
If we look at the bigger picture, then we still see weird stuff like Mike Phelan still staying around, and our supposed technical director in Darren Fletcher now being a part of the coaching staff.
RR interim may be deemed as underwhelming, yet it gets the damage control part right, and this helps making clear that the issue is huge, and no overnight easy fix. The fan and next manager should be prepared. RR enterprise as club building consultant would mean the assessment of the squad and the club would help giving the next manager a head start. This is something you can't expect and get from Carrick as interim manager, who even if he does okay, would likely leave before passing on any insight to the new manager.
If RR had started his consultant role right away, it would be pointless IMO. He would still need time to oberave, get to know people, and assess the inside affair of the club. And without a permanent manager, there wouldn't be much change on our hesitance to buy players during January, and the search for the new manager for next season. Basically RR as a consultant right now would be taking his time watching, and doing talking with the bosses. It would not be much different than from what he's doing right now.