they prevent employees from ever forming a second union if they don't like the first.

Do you have examples of this that actually hold up in court?

Unions also often require non-members to pay dues (the exact term escapes me at the moment, something like 'association fee').

You also still receive all of the benefits though. You just don't get to do union activities like union elections.

Source: http://www.nrtw.org/a/a_1_p.htm "If you are not a member, you are still fully covered by the collective bargaining agreement that was negotiated between your employer and the union, and the union is obligated to represent you. Any benefits that are provided to you by your employer pursuant to the collective bargaining agreement (e.g., wages, seniority, vacations, pensions, health insurance)are not affected by your nonmembership."

You have the requirement to be represented by the union.

You say this like it's a bad thing. The union's entire purpose is to defend its members.

A true right to organize would mean you could have multiple unions with the right to be represented by whoever you want, or no one at all if you so preferred.

What is the bigger number: Five, or One? Excuse the Game of Thrones link but I just don't understand how you think having multiple unions competing against each other helps employees at all. Competition only serves those who benefit from it. You know who benefits from competing unions? The employer.