Well, the "border is the middle of the river". The river meanders a bit, and the water and derbis would kind of tough on the fence, and a hazard to navigation, I think.

Fences would have to be built on the edge of the flood plain, which would effectively cede the whole river and southern flood plain to the United States. Of course, the US could not enforce laws south of mid stream, cuz that's Mexico, and our bad guys could gather would gather north of the fence where, the Mexican police could not get to them, and make faces at the US Border Patrol.

There will never be a fence, in either Mexico or the United States. It's just something to argue about, I think.