There are plenty of advantages to losing this status. Each team in the cartel was always for-profit, but now the central office has zero obligation to report many financial datapoints that would otherwise become public knowledge, so really they don't lose anything. They removed their non-profit status during a modified
http://politicaldictionary.com/words/friday-news-dump/ during the baltimore riots so it barely made headlines. The funny/sad thing is that people are generally so uninformed that the "fake news" aspect where people would claim "nfl teams dont pay taxes" (not true) was picking up steam and hurting their brand more than legitimate gripes about how the league pulls off wage-suppression and other collusive measures that have nothing to do with their non-profit status.