In a nutshell, the MLS Players’ Union is asking for free agency (an end to wage fixing) with no legal leg to stand on.
The MLS was created as single-entity LLC (PURPOSELY MADE TO PREVENT FREE AGENCY!). As a single entity, players do not play for teams, but for the league. As such, since a company cannot collude against itself (you need two or more parties in order to engage in wage fixing), the Players’ Union cannot ask the league to end wage fixing of player contracts and team salary caps. As long as MLS is not working with other leagues to fix the wages of other players’ contract wages to prevent competition, the MLS can set their wages to whatever they feel is fair and let the players, their employees, choose to work for them or not. If the MLS were working with NASL (for instance) to keep those contracts lower, thus limiting competition and preventing players from going to greener pastures, it would be a different story.
Of course this throws a HUGE wrench in negotiations, and it will be interesting to see how the Player’s Union responds.