Not to change your overall point, but you almost never launch west. When possible, you want to launch east, to gain the benefit of the Earth's rotational speed. Sometimes you launch north or south so you can go into a polar orbit which allows viewing more of the Earth. But there's pretty much no reason to launch west. One exception to this is if your launch site is located in a place where that's the only option, which is why Israel does it like this.
For American launch sites, you have KSC for launching east, and Vandenberg for launching south. (North and south are equivalent in terms of which orbits they can reach, so you don't need both.) Vandenberg can be used for launching west, but pretty much never is, unless you count ICBM tests and the like.
I assume the parent poster meant that the launch should take place from somewhere on earth where there is earth 2300 miles out. It's likely not convenient to do so, at least not for all launch directions.
It would be convenient enough but the FAA isn't too happy with the idea of a 12-story missile full of explosive fuel and oxidiser flying over populated areas.
If you just needed to find two bits of ground with room for rocket pads and one 2300 miles east of the other it really wouldn't be that hard to have both in the continental US. It's the fact that the whole flight path has to be safe that makes it virtually impossible.
For American launch sites, you have KSC for launching east, and Vandenberg for launching south. (North and south are equivalent in terms of which orbits they can reach, so you don't need both.) Vandenberg can be used for launching west, but pretty much never is, unless you count ICBM tests and the like.