Lots of good stuff here!
I believe 1.3 was probably the average situation when a large number of aircraft recommended approach speeds was looked at. In practical terms, the manufacturer will recommend a speed for approach which gives satisfactory handling and takes into account the power available. In days gone by, view over the nose was also a factor. In the US Navy, the carrier approach speed also had to be able to cope with a gain of 50 feet by tweaking back on the pitch control and without adding power; in other words, the approach speed shouldn't be too far up the back side of the thrust required curve. With todays hi performance fighters, (eg F18) Vs is actually at a very high alpha, and tail strike would be significant at 1.3!
So with a conventional light aircraft, the manufacturer will probably start looking at the 1.4 area and reduce approach speed until he has a comfortable trade off of all the variables.