The "hand the transmitter to the instructor" works fine 3 mistakes high, but how do you learn how to land? Suppose you're 10 feet off the runway, and the student stalls or turns the wrong way. I don't think the instructor could get the transmitter and gain control in time to save the plane (or worse).

The "instructor fingers over the student fingers" is a personal preference thing. Many men prefer a little more personal space than the method affords, but for others it's very successful.