The cable falls behind the desk because nothing is holding it. That is the whole problem, and it has a boring solution.
What you get
Five clips with a weighted base. The base is heavy enough to stay put, light enough to move when you rearrange.
Placement
Put one at the desk edge where the cable needs to stop. The clip holds the cable at the diameter you push in, so it grips a thin charging cable and a thick monitor cable equally.
One thing to know
The adhesive pad is optional. On a wooden desk, the weight alone is enough and leaves no residue.