Reddit says to only downvote if a comment does not contribute to the discussion, not if you disagree.
So downvoting is an implicit choice of only "good" reasons.
Putting a drop-down list with "good" reasons is as good as displaying a pop-up: "Are you sure you are downvoting for <good reasons>?" - which will be promptly ignored.
Users will just be frustrated for a bit until they train themselves to pick the category that maximizes the effect of their downvote.
The only thing you can do with categories is display the distribution / most prevailing category alongside the score (like Slashdot has been doing for decades).
In all of this, you seem to want to control why people downvote.
Instead, examine why people downvote. Because categories won't change that.
It would be like the emoji committee not including an emoji for penis. That worked well, didn't it?
Unless you add categories like "I think the author of this comment is a moron and I hate them", people will shoehorn your categories for this use case.
And if you do that, I'm not convinced the result will be necessarily positive.