Every business and industry is run differently. You can't paint all unions with the same brush; the way they operate varies drastically.
In many cases right-to-work will cripple unions because if there are union and non-union doing the same job side by side, then there is effectively no more collective bargaining. There won't be any incentive to listen to the union members because they'll just phase them out with non-union. Either that, or the unions will make a collective agreement, and the people who aren't dues paying union members will be getting a free ride.
If you are a union member, you can't just choose to either pay dues or not pay dues. Without a steady, reliable stream of income, the organization will shrink and be severely limited in what they can provide to the membership in all aspects of their operation. It's just like going on strike. You can't have the members who inevitably disagree with the strike keep working or it will undermine everyone's efforts.
A lot of people have a very misguided interpretation of what unions are about these days. All they see every now and then is a blurb on the news about UAW/CAW, CUPE, teacher's unions, and I'm not saying that this is necessarily true, but it comes across as every union member of every union in existence is self-entitled and overpaid for what seemingly little work they do at their cushy jobs. The public sector is one thing, but don't forget that the vast majority of unionized private sector companies have to compete with non-union companies. The fact that they have to remain competitive automatically ensures that things don't get out of hand. And, in this case, if a union employee doesn't want to pay dues, they can always go work for a non-union company.