Wrong way around. Hazard wanted to play centrally, but Mourinho didn't agree. He gave him a run out out in the middle against Liverpool, but then substituted him off. The two fell out for the exact opposite reason you stated.
By the way, Mourinho called Hazard his "new Messi". And yet still played him out-wide.
It's difficult to believe that you're arguing that Messi is physically stronger and a better header of the ball than Lukaku. That's what every centreforward in Mourinho's teams have all had in common. He plays with #9s not false #10s. That's what the word 'system' refers to.