The "right" answer depends a lot on your corporate culture.
My first response would be to tell my boss about the problem. If he can't do anything about it, it is then up to him whether to take it up with higher management.
I definitely would not just start doing these tasks myself unless they were closely related to my current job. At best you are taking on extra work for no compensation. At worst you will get in trouble. I have fond memories of the time I did a task outside my normal responsibilities and I got hauled in front of my boss and my boss's boss for "exceeding my authority". Even though it was impossible for me to do my job if this task wasn't done.
In some companies, pointing out that management has made a mistake could get you in trouble. I recall one job where every year employees were all given a form to fill out where we were asked if we had any suggestions how company procedures could be improved. The first few years I left this blank. One year I wrote that procedures to arrange business travel were cumbersome and suggested some ways they could be improved. I got an email back saying that my boss had explained to me why the current procedures were necessary. No one had explained anything to me, but I got the message that my suggestions would be ignored. A couple of years later I made another suggestion and that time my boss came to me and said that upper management didn't like being told they were doing something wrong and I should fill out a new form leaving that question blank. So okay, fine. I once learned that a co-worker had complained that some employees got special treatment -- I didn't agree but whatever. He got dragged in front of his boss and his boss's boss and lectured about how company policies were totally fair until he finally said, "I guess I shouldn't have written that", which they took as an admission that he was wrong and the company was perfect. And I wondered, After management punishes anyone who says that company policies are not the most perfect that could possibly be imagined, so that the employees learn to keep their mouths shut, do they then congratulate themselves that the employees are all totally happy and morale must be sky-high?
So I'd say: Tell your boss what you see as the problem. If he does nothing or upper management does nothing, leave it at that. If there are enough things like this, that may be reason to quit and find another job. But that's a bigger question.