The fly out feature manager design tree can not be removed. However, it can be collapsed by clicking on the minus symbol on the left side of the assembly name in the fly out feature manager design tree.
For me, that pops up when the regular feature manager is replaced by the property manager. I find it very useful. I don't know how you get along without it.
You can use this when doing certain functions, if you dont want to see it click the - symbol and shrink it.