Well, Sweden's death rate has been three times higher than other countries and hasn't been deemed a success by very many folks.
Just because you don't have symptoms doesn't mean you're less contagious. You can still pass it along to other people who can spread it to other people and still get sick.
As for the NFL, it seems their policies in general are always fairly reactive and public relations oriented. Concussions, race, etc. all are only summarily dealt with when the PR hit becomes too much to ignore.