I read that same article, but there are all sorts of problems with that approach. It depends on how hard of stance the players (and potentially the government) want to take.
If the union disbands and there is no CBA, then all sorts of things we take for granted could be in trouble. Take for example the draft. The rules are such that when a player gets drafted, the 32 owners and the league agree that that player can speak to and negotiate with only the team that drafted him, no one else can talk to him and he can't talk to anyone else. Essentially you have 31 owners all agreeing they won't talk to him. It's actually the textbook definition of collusion and collusion is illegal at face value.
But then one may ask: How do they currently get away with doing something illegal? Well, it's not illegal if it is something collectively bargained. Also (and here's where the government comes in) there are various anti-trust exemptions for professional sports. Earlier this year, the US Supreme Court ruled that the NFL was indeed 32 separate entities, not 1 single one. The potential ramifications of that ruling are huge if there is no CBA.
If there's no draft, there's no NFL. Its as simple as that. Its pretty much the only way the small market teams have of bringing in talent.
Can you imagine the attendance of a small market team, when they went 4-12 one year, and can't convince any decent players to sign because they can't afford to compete with the big market teams, and they can't win?
I think you'd see 6 teams fold in the first 5 years, and you'd be down to about 16 teams in 10-12 years.