In Reddit, there is a section for posts that are heavily down/upvoted, making them "controversial." Why might this be a bad idea?
Once you have earned 1000 points on a Stack Exchange site, you can see the vote counts. You can click on the score of a post, and see how many upvotes and how many downvotes the post has.
The reason that this is a privilege, is that it was (and probably still is) a somewhat expensive database query. So Stack Overflow (the company) tries to limit its use a little. Similarly, this "controversial" tab would probably cost a bit in terms of database usage.
More important, however, is a practical side. Sites like Reddit benefit from controversy. They are about discussion.
Stack Exchange, on the other hand, discourages discussion. It is about getting objective answers to objectively answerable questions. Controversial posts aren't helping the mission. Drawing extra attention to them just draws in even more people to add to the controversy, rather than resolve it.
I don't think the use case behind why a post might warrant an up-vote or down-vote is consistent enough to necessarily call the underlying issue "controversial".
Sometimes a down-voted post can be fixed and the voting turns to the upside. Sometimes the voting is split between "this question is poorly asked" versus "I'd just like to know the answer". Sometimes communities simply disagree about what is on topic, and then there's the old guard who may have become weary of seeing the same issues come up again and again; those are just aggravated down-votes for the lack of research effort.
But that doesn't necessarily make any of these questions controversial. And I'm not sure what folks would do with that information necessitating that we call them out in a separate tab.