And sport is a private sector activity -- why should the government be involved?
Only US citizens should recite the pledge of allegiance. Non US citizens owe their loyalty to another country. But schools don't do that, because it would mean identifying US citizens.
I'm firmly convinced that no child, citizen or not, should engage in a daily ritual like that, especially not at school. The worst aspect of contemporary education -- not only in the US, but in many other countries -- is teaching through indoctrination. Instead of encouraging our kids to develop their critical thinking, our educational systems focus on making them learn by repetition and trust the authority.
These differences my seem subtle or even trivial, but history has shown that it is dangerous.
Note that in the US soldiers and other holders of the public trust swear to uphold the country's constitution, not its flag.
It all comes down to the order of primacy: the country, constitution, civil institutions, chain of command etc are all in service to the support of the citizenry not the other way around.
Individually and collectively perhaps, but not only the Republic.