No, because it introduces the free rider problem. It creates an incentive for any particular union member to defect from the union, because they no longer have to pay fees, but are legally entitled to whatever the union negotiated for.
It's like a law that prevents compulsory membership in a fire insurance plan, but also allows you to sign up for retroactive fire insurance after your house burns down.
> but are legally entitled to whatever the union negotiated for.
How so? Wouldn't they be independently discussing their salary with management at that point? What law guarantees that non union workers get the same benefits as union workers?
Thanks to the National Labor Relations Act, if a union represents >50% of employees of a company, then the union's negotiations apply to all employees.
So, you have an incentive to not pay union dues, as whatever the union negotiates for, you will get without paying a penny. Not to mention that if there's a members-only agreement, where members get more pay/benefits/etc, this creates a reason for an employer to not hire union.
Due to this, unions can't really fight for members-only agreements.
Even if it weren't repealed, non-union members would still freeload off the work of union members.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.)
[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.
It's like a law that prevents compulsory membership in a fire insurance plan, but also allows you to sign up for retroactive fire insurance after your house burns down.
It's sole purpose is union-busting.