Especially with free agency, a football fan does not identify his passion for a particular player(s). Rather the fan has passion for a team/city for which they root for. No way a start up league could take on the NFL. Yeah, maybe today's stars would start a new league, but they would be taking a huge pay cut and the league, like a typical new business, would take years before becoming profitable.
The NFL on the other hand would be able to go get the top college stars to come to their league because that's where the money is. Today's NFL players would not be able to convince college kids to stick it out before the new league became what the NFL is today. It has taken the NFL 85+ years to get to where it is now, if the new league took 10% of the time to reach that level, you are looking at almost a whole generation of players to sacrifice. Not going to happen when there's a viable option already.