Nope. Both aspects are criticized on their own right. Even if we leave alone the recruitment part, for his supposed coaching how many of our existing players did he improve or for that matter how many of his own signings have been playing at their best.
You cannot just say that his main job is coaching and management of the team and ignore that he is failing at that too.
This thing about improving players has to die. Barely any managers come into a club and turn average players into good players, let alone coaches trying to dramatically shift the style of football and under the pressure United managers have to consistently win matches.
Klopp didn't achieve anything until he was able to reliably move on from garbage/average players like Agger, Sakho, Moreno, Clyne, Lucas, Can, Lallana and Benteke.
Howe's Newcastle shit the bed in almost any game they have to rely on the likes of Joelinton, Almiron and Longstaff to be the main men.
Even Guardiola quickly moved on a fair chunk of the players he inherited at City, a squad that was literally being assembled with him in mind.
I'd also argue that we have seen improvements from some players. Wan-Bissaka and Dalot have both looked far better for Ten Hag than they have for previous managers. The issue is that they're shit. Fred (at times) last season and McTominay this season have looked more competent than they have before, but they're both ultimately not very good midfielders. Harry Maguire has literally come back from the dead this season, and Lindelof has looked nowhere near as calamitous as he had previously.