In my plan you could join ANY unions, even Republican Conservative one. And you could organize the new one.
Your plan is idealistic and impractical. It takes away peoples' individual freedom and makes them just more pawns of the collective. Whether that collective marches under the banner of socialism or conservative republicanism, it is still a collective. No thanks.
Why should an employee have to be a member of a union to negotiate with management? Under unions, stellar employees have no incentive to achieve, since they will receive the same wages and benefits as those who sit around with their feet up all day. Leeches have no incentive to do anything, other than when the boss is around. This affects productivity and reduces the company's flexibility and opportunity to earn profits.