They are powerful but not unaccountable. Every time a union strikes they use up some of their power, both with the general public and their members (who want to work!).
In the case of many public unions they are legislatively prevented from striking.
The idea that unions are the ones with significant leverage over their employers in this day and age is baffling. Just look at the railroad workers who got manhandled by a Democratic government!
If there are not enough jobs in the area and not enough capital to kickstart businesses, the people in that area are in a situation where something is better than nothing. So a corporation can come in, offer below subsistence wages and the people will feel as if they have no other option. It's not what the labor is technically worth because the value produced by the labor far exceeds the wage given to the laborer.
Individual laborers have no power to fix this. The employer can fire them and exploit the next desperate person. They can even cycle through back to the original person as they get more desperate.
Collectively, the laborers can do something. They can redress the balance between laborer and owner. But only as a collective. The minute the individuals are allowed to operate independently, the old system reasserts itself.
Stop carrying water for people who won't even allow you a drink for your efforts.
They aren't "a part of" schools and corporations, they are the schools and corporations. It is obvious why 90% of an organization can make a decision to shut it down. When unions are smaller and don't constitute such a large portion of an organization, as will be the case with Tesla, they are not able to shut it down.
In the case of many public unions they are legislatively prevented from striking.
The idea that unions are the ones with significant leverage over their employers in this day and age is baffling. Just look at the railroad workers who got manhandled by a Democratic government!