SAG/WGA controls the creation of near endless amounts of original content. Without them, studios lose nearly a trillion dollars in potential revenue.
UAW members assemble for the big 3 automakers and can lock down any plant they choose causing billions in losses. Same goes for Unifor in Canada and the unions in Mexico.
They really don’t need public support. But then the public itself is not getting paid either. So it’s very easy to sympathize with fellow underpaid workers.