My girls are older (21 & 16), but they are extremely opinionated about things like this. I am certain they would have been saying no to everyone just on principle even if it meant there would be disciplinary consequences from the school. There's absolutely no way they would have allowed themselves to be coerced into dancing with someone.
I know they mentioned curriculum in the article, but it really is not clear. To me, it sounds like they are learning different types of dance in PE and then having school dances (for fun) where they're hoping the kids will use some of the moves they had learned in class (but the dance is not actually part of the class grade). I think it would be fine to be assigned a partner for class, but I just don't like the feeling of not being allowed to say "no" at a social dance event.
I also don't really see where this policy would eliminate rejection or make kids feel better about themselves overall.
By removing the possibility of "no", the boys will be emboldened to ask girls that they would not normally even consider. So won't all of the pretty/popular girls be receiving all of the invitations? I would think this would make the rest of the girls feel even more rejected and worse about themselves.
I think it's pretty common. I had dances in middle school and my kids did as well.
Most of the ones in our current school district are right after school and there are other activities (food in cafeteria, basketball, etc) so I don't think there's much actual dancing going on. All of the schools do have an 8th grade formal that includes dinner and is more like a traditional dance.