... one interesting thing that was brought up was that there are states... that are not allowed to strike, like Chicago and Washington DC.
Well, Chicago and Washington DC are not exactly states. Sorry to be nitpicky. If strikes are illegal in those two cities I'm surprised to learn that.
President Reagan fired air traffic controllers for striking because that job was so important to the US's infrastructure.
The U.S. President had authority to fire air traffic controllers?
As for whether Public Transportation employees should be allowed to strike, I would say Yes, but I would encourage such employees to use a strike only as a last resort. But then I suspect they would anyway, since no one really wants to go without receiving a paycheck for a long period.