I think you are confusing terms. Closed (only members can even apply to work) shops were outlawed in the us in 1947.

24 states allow Union shops (workers must join the union after hire).

In theory multiple unions could strike together. Alternatively, dissenting members of a single union can keep working.

In both systems striking is the union leverage.

Ah, I missed the difference between union shops and closed shops.

But that alternative of dissenting unions not striking is exactly the loss of leverage that I was talking about.

Multiple unions striking is not just theoretical but the norm i Europe. There was a large strike against Tesla in Sweden. Many unions across the supply chain joined the strike in solidarity.