This is more a general automotive question, but I do own a Honda, so I
thought I'd try it here.

Growing up, my father always told me to engage the parking brake on a car
with an automatic transmission while the car was still in drive or reverse
(or even neutral) before shifting into park (of course, the car should be
stopped). This was somehow supposed to "reduce the strain" on the
transmission. So, is there really any good reason to do this?