I don't disagree with the premise of your argument. And the solution is to hire more staff so individuals aren't put into these positions. The trade off though would be that you need to pay everyone less, reduce overtime, etc. so that the overall cost of doing business doesn't go up.
The problem becomes that this argument never works with any union, whether it be teachers, nurses, police officers or any other "critical" group of employees that serve the public. If a union is offered the choice between more pay for current members, or no raises but hiring more people to reduce burn out, overtime costs, increase safety, etc. what does everyone think the union will always choose on behalf of their membership?