Sorry for the scattered posts on this topic, busy schedule so I'm having to circle back here.
I certainly don't mean to argue that public employee unions don't matter at all when it comes to employee terminations. They do, they just don't matter for the reason people think they do.
The rights of public employees exist with or without unions though. What unions can do is provide resources, expertise and (sometimes) representation to help employees enforce those rights. You can have all the due process you like, if the employee doesn't understand the applicable rules they are at a significant disadvantage - just like any pro se litigant or defendant would be.
Public employees who have union representation are likely more effective at enforcing their rights than non-union public employees. But I have a hard time begrudging anyone, public employees included, who chooses to enforce their Constitutional rights.
Maybe you don't think they deserve those rights. That's fine but you should argue against the rights as they exist and not against an organization which didn't create the rights and only serves to enforce them.