No; starting late is bad news for after-school sports, especially on meet/game days.
Not important. High school sports should be deprioritized.
Considering the significant problems that America has with obesity and similar issues plus the wider issue of inactivity in the West generally; I would argue that sports and exercise should be seen as something that should be prioritised. Generally if you encourage exercise at a younger age its much more likely that people remain active in the long term which is incredibly beneficial both for the individual - more likely to lead to a longer, healthier life - and for society as a whole - cuts healthcare costs and a healthier population tends to be more productive.
However, it could be argued that sleep deprivation makes people too tired to exercise.