Jerusalem was also in the "wilderness" (and still is) due to her apostasy AB, for killing the prophets and various other indictments, so this argument of yours holds no water.
If this was written when Israel was in the wilderness, then that makes it written after 70 ad, in order for Israel to be in the wilderness.
The harlot mother is not Babylon as in the tower of babel, John is specifically equating apostate Israel with Babylon, Sodom and Egypt, because they had become all three (and still is).
it looks good and it is good - I haven't seen anyone successfully argue against it...