Unions can and do stand on their own. If a union has won, through an election of the workers at a business, the right to be the sole bargaining agent for those workers, union membership becomes a condition of employment at that particular business. To give each new employee the opportunity to not join, but still benefit from the gains the union has made, takes away the choice the majority of workers have already made, and makes them chumps for the new employees. It is basically unfair.
This whole argument is about the survival of the middle class. Without unions, or if unions are weakened to the point they are irrelevant, as the right to work for less does, the survival of the middle class is in peril, and we become a country that looks much like Mexico. Extreme wealth on one end, and extreme poverty on the other.