Korea has already started their football league. However, if we are talking about the 3 main countries, then yes, it would be. NRL and AFL have always generally been the type to do otherwise.
As for the schooling part, education will not suffer. Online classes are very easy to access and conduct nowadays, but like Kriterion says, it will be the interaction that suffers. That hanging out with friends and being able to play together. For families that have a decent size yard and more than 1 kid, that is not too much of a problem. In Aus now with restrictions easing, you can at least visit friends within the restrictions, so the arguments for keeping schooling open are starting to be very weak (even when they weak to begin with).
Medical services will struggle however, and there is other industries like travel and tourism, hospitality, events, mental health that will also suffer. If doctors and nurses are infected, it creates a problem. It also creates a problem in the sense of other surgeries and medical being put off and delayed, as happened with my surgery. Essentially, this creates a back log in terms of the medical side, and there is obvious risk in rushing through a practicing or trainee doctor/nurse to work on the front line. The. other services will suffer from the obvious drop in business, and the longer they stay closed, the harder it is to recover. Opening too soon however will cause a second wave and the effects will then be felt far worse than currently projected.
The damage has already been down in the US, and when you have a select dissident people becoming a law un to themselves, it creates a problem for the rest who want to do the right thing.