Trying to satisfy everyone and hence geting the work done by everyone is one of the management styles. It cannot be concluded as wrong as its one of the styles afterall. But, I think, one fundamental fact strongly prevents this particular style from entering the list of the best management styles. And that's as following.
Do whatever you can, you cannot actually satisfy everyone at the same time!
All that you do defeats your own idea of doing so and that the work you think is getting done by everyone might not be as qualitative as it is supposed to be. Hence, what I understand is that one must differentiate people for their capabilities and efforts. Rewards always lift the energies to the next level, however small or big the difference is. Doing things right in that regard is very important rather than just completing them.