My thought is the semi-uprights crowd out the other, more natural and symmetrical branches. Also, I am worried that they are not structurally sound and if they split from the trunk I will lose the whole tree because of the way the branches interact with the trunk.
My worry on cutting it is similar to it's breaking off: If this section is cut, the trunk will reject nutrients to a large center section of the trunk as part of its natural defense. That is what I mean by "wall off"
I'm obviously not an arborist, but it appears to me that there is some seperation of the wood in the trunk leading to what i refer to as the semi-upright branches. I may not be explaining it correctly, or I could be off base, but I am concerned and want to do what is best for the tree. The tree is partially growing over my house as well as my neighbors, so I am concerned about structural problems, as well as tree preservation. I just moved in an had to take down a 40" diameter willow that was on the other side of the yard due to hazzards with the house on the other side.