The reason might be that union members give a percentage of their income to a governing body which is barely distinct from organized crime in which they have no say in. The federal government already exists. You really want more boots on your neck?
I kinda agree with you, more boots is not really an ideal way to achieve this. Worker protections should come from the government itself, so much so that there is no need to form unions, like how it is at many places in Europe. I don't see how that could be created in the US though. I think trade unions are more their vibe - or not even that, of course, like in case with you. And of course, in US history we can see how some organization grow and get a life on their own, like the NRA. Not necessarily remaining on the path to protect past principles, or the welfare of the people.