I can see many positives to standing desks like the ones you outlined but I think that ultimately (at least at the current time), they would create more problems than they solve. For one, they may make it more difficult for teachers to manage loud and rambunctious classes and put a stop to mucking around. When a class is misbehaving, generally teachers many tell them to sit down and do some work as while they are standing up they are mucking around. Even with standing desks, there is no guarantee that the mucking around would stop.
However, I do think it is important to address issues like obesity and poor posture, however, I believe that at present there are other alternatives. I think that perhaps having more sport in schools as well as generally better access to healthy foods and less junk (I know our canteen is mostly chips, chocolate and cake.) may help to address this. Our school has also introduced ergonomic chairs that really help with posture.
Another aspect to consider would be the cost of replacing current desks if this was to be immediately implemented and the waste that replacing so much perfectly good equipment would generate.