It sounds good. Right to work yes? Increase choice and all that.
The issue is that in the first place it's an intrusion of the government into an employer/employee relationship. Usually conservatives oppose this. That they often support right to work laws should tell us who such laws are likely to assist. Hint..not workers.

It is already illegal to be forced or coerced to join a union.
U.S. private sector union membership is at all time lows.
Even in Michigan which is ground zero for the modern industrial labor movement total private and public sector union membership is around 17-18%.

What right to work laws do is attempt to use individual incentive and interest to defund the union. See, when a union wins the right to represent workers it can not legally restrict benefits, wages and working conditions to dues paying union members. That's against the law. Companies normally pass on whatever they give to union workers to non-union workers in an attempt to limit or prevent union growth.

So there is an incipient "free rider" problem. If you can get the benefits without paying the costs, why wouldn't you?
So unions not only collect dues from members but are also legally allowed to get "fair share" of costs of representation from non-members on the job.

Right-to work laws indicate that these fair share/union dues may no longer be automatically collected. If you don't want to pay your union dues or your fair share, you don't have to do so.

This means worker A who hates unions but enjoys a union standard of living doesn't have to pay for it any more. Worker B is a union man thru and thru but is also nobody's sucker. So he may tire of paying for his cost and worker A's as well. So eventually he stops paying. New workers see no benefit to joining the union and so don't. Over time the union loses the financial ability to do ANYTHING. And just as importantly as fewer people are actually IN the union, the union loses the political and legal ability to represent workers at the workplace. So goodbye union. And then the company is free to show a different side of its personality to its workers.

Unions are not nation states of course but imagine if the US had similar laws around taxes. If people could decide that they didn't want to pay taxes for national defense but also didn't want to leave the US, eventually the national defense system and finally the US would crumble. This is classic free rider economics.

The states who have adopted "right to work" laws tend to be states with worse outcomes for workers.