Should one of the legs be in full contact with the court?
The only way a leg could be in full contact with the court, is if the court were a duvet or table cloth, wrapped round your entire leg.
The words of the rule, in this regard, are far more accurate and clear than the words you use.
"some part of both feet of the server and receiver must remain in contact with the surface of the court "
So any part of the leg above your feet don't have to be in contact with the court.
And it doesn't say the whole foot has to be in contact. Just part of both feet.
It's one bit of the rules that they've actually written reasonably clearly!
So it's allowing for, for example, the back foot to pivot on the ball of the foot. And it's allowing the front foot to shift the heel and then go flat. So it's allowing a kind of back and forwards rock and pivot to take place on the feet, for the serve(that we see on forehand high serve). That'd be why they talk of part of the foot. They mention stationary but they must be allowing for that rock-pivot movement at the feet, 'cos it's so standard and so must be why they mention part of the foot. But a foot can't come off the floor or slide along the floor, before contact. as, I doubt they'd count sliding as stationary.