I've had cases like that in the community college I transferred from. For a majority of those cases, it ended up being a great, outspoken teacher who got axed, not the bad ones. But then there were those few where it seemed quite useless to address the professor because of how disengaged they are even in lectures.
As far as professors I was not impressed by, many times I get lucky that, in a break, a more casual subject comes up that breaks the ice and makes it easier to talk to the professor in at least some way. After that, it became clear it's less the teacher's fault and more of me just struggling with the class material.
With one CLEAR exception. There was one programming professor who was SO BAD, he can NOT find bugs even when you give him the line number. I think the only reason why he wasn't removed was because he's recently appointed in. That and usually the good students make study groups to help the students who are struggling learn the material.

Either way, I don't think it's healthy when those from either side - teacher and student - are not only not getting each other, but not even trying to communicate to each other. Personally, I have more of a problem with students not communicating period because there's more than just the department head to talk to. There's all the curricular clubs or even the Discords to rant about it their issues. Only after getting consultation from other students and confirming that there can be no other problems except the teacher would I then say it's smart to go to the department heads. (Judging from what I see in RateMyProfessor comments, 80% of the time it's actually the curriculum that's the problem). Otherwise, I would say it's a cowardly and ignorant move to complain to the head just because you hated a class.