“The union do represent all members of the bargaining unit whether they are members of the union or not.”
Why? Who imposed that restriction? Was it the unions themselves to prevent non union members from making their own deal with the company?
“Non-union members cannot for example go to management and negotiate their own terms of employment if they are covered by a contract.”
If this is a rule imposed by the union, then it’s really the non union members that should be complaining, since it restricts their freedom to negotiate their own deal with the employer.
I am not a labor lawyer but the National Labor Relations Act of 1935 also known as the Wagner Act set up the labor laws of the US; that act also created the National Labor Relations Board, the NLRB. Federal statues gave the right to a union to represent all members of the bargaining unit whether a member of the union or not. If a non-union member who is covered by a collective bargaining agreement attempted to negotiate on his or her own behalf, wages, hours, or working conditions, the union could file an unfair labor practice with the NLRB or
equivalent state labor board and would most certainly win.
A better performing employee should be able to strike a better individual deal. The terms and conditions of that deal are privately held and no business of the union.