My understanding is that many school districts in the U.S. have now either seriously restricted, or outright banned, teachers from touching students, except in emergency cases. Even the “healthy physical affection” that the OP suggests, may be a thing of the past in many districts.
My wife is a former elementary-school teacher. There’s a television ad currently running, for a prescription asthma medication, in which a high school teacher is walking through the school, interacting with students. At one point, she uses her hands to gently push apart a boy and a girl who are standing close together; my wife saw that ad, and said, “she’d never be allowed to do that in a real school.”