Common misunderstandings...
At will employement is a contract. And like every contract there is an assumption of good will on both parts. There are plenty of reasons why an employer cannot fire an at will employee (race, religious affiliation, age, etc etc). The result of that, is that most companies union or not, will have a well documented file for any firing, and state a reason for that firing.
Secondly, if you are a union airline employee, you dont have a contract with the company. You are part of a collective bargaining agreement, and are indeed, an at will employee. You may quit at anytime, and you may be fired at anytime. The only thing the union does for you is provide you with representation, in house or in court if neccesary.
So, basically, union employees are no different than non union employees, other than that all union employees in effect have union lawyers/representatives on retainer, paid for with their dues. The effect of that, obviously, is that companies with union employees are more inclined to prolong a dismissal, knowing that the effected employee will definitely have representation.
Whether either process benefits any individual employee is debatable. For example, if the process results in the firing of a good employee that has a personality conflict with a manger, that's bad. If the process protects a slug that is pushing his workload to you, or worse, endangering your safety, that's bad too. Both happen in either situation.