The leg press is “unnatural” in a much different way than the squat is “unnatural”. The former departs from normal human biomechanics, whereas the latter departs just from any particular sport or activity. This invalidates your analogizing about the two-factor model.
Practically speaking, the leg press is useful only if you’re detrained or injured.
I would actually be very interested to hear even an anecdote about a person's squat going up due to work on the leg press for longer than a few weeks
McBee, what do your lifts look like and how do you train the leg press?