I wouldn't say that Real Madrid refused to fight for Haaland, but there have been a couple of things at work and I believe as a player at that stage one of the dreams is to be coached by Pep Guardiola for sure. There have also been a couple of other things like Haaland's father having played for Manchester city for example and for a guy who is so competitive like Haaland, I expected that he will prefer the Premier League over La Liga. And he has done everything right, I think he had that feeling and to be honest who wouldn't like to be part of the best club in the world. The Manchester City squad is the strongest out there right now.
The decision of the player and his agent plays a major role in the choice of the club during transfers. Many players have even gone to the extent of reducing their pay because they want to play for a particular club. The English Premier League is the most exciting league in Europe and many players desire to play in the league. Last season Real Madrid had a striker that can not be benched because of Haaland. Benzema was a highly respected Madrid striker that is seen as the face of the club. Haaland would have had to rotate games with the world's best footballer. But in City, his place was guaranteed because they were willing to give the Norwegian striker all the attention he needs.
I don't think they would have made Haaland rotate with Benzema. Maybe sometimes, but not as a golden rule and one reason why Benzema left the club (besides the money) was also that he knew if Real Madrid signs a new striker that his time has come to be sitting on the bench more often.
And a striker like Haaland wouldn't have accepted if the new club tells him that he might be sitting on the bench even when he is not injured. There is no needfor him to hold back. His numbers are so out of this world that no club could expect Haaland to sit on the bench. Unless he doesn't score in many games of course, but that is not the case. He scores like a machine and he got all the trust from Pep that he wanted as a striker. Even though the system City is playing might not even be the best for Haaland and Real Madrid could have been the better place only in terms of the system they are playing, not in terms of the overall success as we have now seen with the treble and Haaland breaking those records.