Yup, I agree with that and wanted to say that too until I saw your comment. I also can say that it really is because my older sister does ballet and it takes a lot of energy and strength and time, It also kind of ruins your feet. School would also give her a pass for gym class and give her credit because of how much effort ballet was.
I like that ballet is cool to watch and a really cool art while also being an amazing sport. You never see the hard work either, Only the outcome.
The exact definition of a sport is:
an activity involving physical exertion and skill in which an individual or team competes against another or others for entertainment.
An activity involving physical exertion - check
A skill in which an individual or team competes against another or others for entertainment - check