I tried a variety of heights. I found that an approximately level strop worked easiest for me. Mounting the hook a little higher (on a towel bar) worked next best. Mounting the hook low (door knob heigth) worked the worse for me, but better than super high (armpit high).

I found the perfect height for a level strop is to mount a U-shaped "robe hook" from the hardware store so that the bottom of the U is level with the bottom of my elbow when my arm was bent at a 90 degree angle. Since the U is approximately 1-1.25" tall, and the ring on the strop slides, the strop height self adjusts to whether I'm barefoot, or wearing slippers

I suspect the old-time barbers mounted their strop to their chair since it was more convenient than walking over to the wall.