What does the employer have to go through the union for?

Benefits, and depending on the union's rules, salary adjustments. Some unions also require informing them of schedule changes.

The reverse is also true, employees may need to go through the union depending on the union's rules.

If the employer is rocking, why would union members vote to strike?

Idk, perhaps communication issues w/ management? Over-zealous union leadership?

The point is, the employee isn't empowered here, they're subject to whatever the union agrees to do.

My uncle went through multiple strikes, few (if any) he actually agreed with, but had to deal with being out of work. He wished he wasn't union so he could just continue working.

the way corporations are structured makes it incredibly easy for that to change

Sure, which is why it absolutely depends on the type of organization. Something owner-operated has a much lower risk of unexpected awful changes than something publicly traded.

A lot of owner-operated businesses don't intend to sell to someone else, the owner will just shut it down when they're done operating it. So "long term" in this sense is until the owner retires. And if they do intend to sell, they could at that point encourage the employees to make any employment adjustments needed.