In the case of copy and paste were you don't want to navigate to another directory in the original dialog; you must have at least two windows open. One with the path of the source and another with the path to the destination.
Tree view, while it may be a nice feature, is certainly not required to keep track of multiple paths in a graphical manner.
I am not defending the removal of the tree view or diminishing the desire of others to have such a feature. I am just saying that it's certainly not required to keep track of locations as I have not been aware that Nautilus supported tree view for many many years and it has never occurred to me that it's missing any functionality nor has it diminished my ability to copy and paste between different directories.