I just don't think that's going to bring more eyes to the sport. The sport is already so damaged with doping, both cases and allegations, having the fox watching the hen house while we all pretend there isn't a problem isn't going to work for cycling the way it "does" with the NFL.
There already is a riders union, the
CPA. The problem is at almost every juncture they have sided with less testing, and defending cheats and dopers, with little focus on some of the other problems associated with cycling and no solution towards stopping doping on their own. Thus, they've been on the losing end almost every time. It's damaged their cause, whatever that cause is. There is also the AIGCP, which is the team's union, which is however run by Eric Boyer, who is anti-doping. The AIGCP however did support the riders decision last year in the Tour against banning race radios. Something again most fans disagree with the riders on.
However, if you are stating the riders union, if more focused and less stuck to a primary cause of upholding the omerta, would lend some outside scrutiny and oversight to the UCI and Pat McQuaid, then I would like to think this would make the world a better place. However, the biggest problem with McQuaid's UCI is the near arbitrary testing and rulings regarding doping, and the CPA isn't going to do anything to remedy that. At least not at this point in time.
The best of all would be a rider's union that is anti-doping, and looking to hold the UCI to seeking third party, objective oversight at all times. But that's about as likely to happen as the NFL joining WADA, as you say.