I'm not overly convinced by that argument. What big players are we talking about? Have United approached them, and are they stalling because the player is waiting for Man City or Liverpool to pick up the phone? Teams that have pretty settled squads, and even if they were interested in a player in a particular position, it may be as part of a squad rotation role rather than an almost guaranteed starter.
The likes of Klopp and Guardiola have has all season to assess their players, and will have had a plan many many months ago as to how they'd like to freshen things up. This has allowed them to act quickly in the transfer market. United have not had that, certainly de Hag hasn't. Furthermore, Utd need more than just "freshening up" the team. As stated, they need open heart surgery. It isn't really about going out and buying the best players in the world. They need to build a functioning team first. Build the foundation, before adding the flare.
United have been rubbish for years, but still attracted big names / players with good reputations. Pogba, Zlatan, Matic, Lukaku, Bruno, Maguire, Cavani, Ronaldo, Varane, Sancho, etc. But, look were that has got them. On the most part, highly rated players sent out to play like headless chickens. And, even when Utd were at the top, they failed to attract everyone. The likes of Shearer, Gazza, Kroos, Ronaldinho, Bale, Hazard, Kluivert, etc. I've no idea how far negotiations went with all these players, and how much was fuelled by media. But, the point is, individual players will also have a wide range of reasons to want, or not want to go to a club. So, I certainly do not expect a guarantee that every single top player would wish to go to United, just like I wouldn't expect them to 100% want to go to City, Liverpool, Madrid, Barcelona, etc.