Once upon a time, I was very frustrated with a certain work policy that was bad for my team. Everyone hated it, but knew it would never be changed.
In discussing it with my mentor, he pointed out that my frustration was really two-fold. First, I was frustrated with the policy, and second, I was frustrated with my own inaction to try to change it. He was right.
He coached me into taking action even though I felt powerless to achieve success. And it worked! My frustration was less because I tried to influence things for the better. This can work for you too.
There is honor in this selfless act of leadership and you will be a stronger and more influential leader for it. Besides, once-in-a-while you will succeed at producing the change you seek - simply because you tried!