Ours does and to be honest, it irritates me a bit! I think 'swappables' can be a useful way of making friends with others, learning 'fairness' and what's a 'fair trade'. I know why they do it but could they not set down ground rules? Like you can only trade within your year group and only at certain times? They also banned tamagotchi, but YEARS ago when they didn't have a pause mode! DS1, in Y2 at the time got to know all sorts of different kids through 'connecting' with them in the infants playground, and I seriously don't think it did any harm. Yes, they had to be on pause mode in class but they're small enough to be left in a pocket.
What does your school do?