Even if it weren't repealed, non-union members would still freeload off the work of union members. Let's say that a union forms, and persuades management to fix a light switch that gives you electric shocks every time you flip it. [1]

Management agrees to fix the light switch. They most certainly are not going to fix it in such a way that it only shocks non-union members. This is an example of a employee gain that was only possible because of a union, but benefits all workers, union or not. [2]

The problem is not the NLRA, it's the right-to-work-for-less legislature. It deliberately undermines collective bargaining from the employee's side (But does nothing to hamstring collective bargaining from the employer's side.)

[1] I kid you not, this has been an actual issue at a McDonalds, which unionized. http://www.themilitant.com/1998/6232/6232_27.html

[2] Back in the day, workers would be locked inside their workplaces, so that they couldn't leave work early. Unsurprisingly, when fires would start, they would burn to death. Unions eventually fought for protection from this - a protection which you, a non-union member now benefit from.