They've made the correct decision imo, and if they give him the right players in the build up phase I believe he will get the team playing the way he wants the team to play which is to dominate the game in all phases of play.
You can't play that way if three of your most prominent ball players (Martinez, Shaw and Mainoo) are not available for a significant part of the season. Mainoo isn't someone that many people thought was going to feature much this season but it was clear to see that ten Hag was entrusting him to play a important role in the build up phase. You don't sign players like Onana, Martinez and also promote a youngster with the skilset of Mainoo to then ask them to play in transition. You only resort to playing in transition if the build up capabilities of your own team become weak against the threat of the opponent's high pressure tactics. And with the injuries United had at the start of the season, it was clear that our build up capabilities were weak against teams who were adept at applying a well coordinated press.
So ten Hag clearly adapted and looked to go direct with the press and counter press as a defensive mechanism high up the pitch. It didn't work effectively but for me it would've been cowardly to resort to type and sit back in a double pivot because that is a strategy that may help us get a few points in the short term but won't help us in the mid to long-term as far as implementing a proactive game style with and without the ball.
I'm not sure how the likes of Thomas Frank became options after what's been reported in the media about INEOS wanting to implement a possession based play-style. Frank and Brentford have been signing players for a direct high intensity pressing game with players with physicality in advanced areas. It's no surprise that Chelsea went with Maresca, because Maresca is a coach who wants to play out from the back and adheres to the positional play principles. And with Chelsea having spent huge amounts of money on players like Caicedo who was statistically one of the very best in the league at evading the press in the build up phase and also signing Enzo Fernandez who is a player that is very capable on the ball dropping deeper, it made zero sense to keep Pochettino or hire Frank.
Erik ten Hag is absolutely a coach who wants his team to dominate the game in all phases of play. Give him the players that are missing in midfield and at CB, and I believe we will see his vision come to the fore. If it doesn't then we can move on from him.