As
stated elsewhere, the Fighter Class is too diverse to be condensed into just three Enhancement Trees. This is an opportunity to build up an entirely new tree, rather than attempt to pack in so much into one changed tree.
Having said that, Monk should not hold sway over a Fighter enhancement, if you are staying with only three trees and not expanding to 4 or more. All monk related requirements or flavor pushed into Fighter Class is beyond silly. If you want to play Monk Class - then play Monk.
As for multi-classing, I will repeat something from many posts on the Council - multi-classing should not be built into any Racial tree. It is Serendipity that should be preserved for when one chooses to splash Classes in the multi-class process. The Fighter tree should be built to make a pure level 20 Fighter viable, with a logical progression of benefits and rewards for continuing on the path to level 20. There has been far too much tweaking, for too long, to take in special considerations of special/unique multi-class splashing. I see Kensei as the ultimate example of this, where Monk infected the tree to this point.
In fact, I'd rather the tree not even be named Kensei, if we only get 3 trees in Fighter. Name it "Weapon Master" or something, and remove all Monk factors.