The hangup with sports reopening, from my point of view, continues to be issues with scheduling. If teams are truly testing all players and staff every day or every few days, they will probably be able to overcome a handful of players on a given team who get sick. But even with testing, what happens if half a team or whatever gets infected within a short period of time (which is possible even with mass testing - someone in South Korea just infected like 50 other people from a single night of clubbing and bar-hopping)? Either the league has to basically say, "sorry sucks for you" and force the team to forfeit or play with basically a replacement-level squad for 2 or more weeks or the entire schedule needs to get re-done, neither of which seems like a great option. But at the very least leagues need to grapple with this potential and for now at least it doesn't seem like that is happening - rather, the leagues are just taking a "let's just hope that doesn't happen" stance which seems foolhardy in the extreme.
P.S. - the NFL's suggestion that they could address issues by pushing back the opening of the season a few weeks is laughable. Do they really think that somehow the virus is still going to be prevalent enough in September that playing games is ill-advised but somehow by October it will magically have gone away? If anything, the league may want to consider starting earlier and building in a bunch more bye weeks to deal with the inevitable scheduling challenges and to minimize gameplay and travel in the winter months when we are very likely to be looking at least at a minor resurgence of the virus at best and a full-blown second wave at worst.