That's sort of what happens on reddit.

Often I feel it's not worth replying to obviously wrong stuff because it'll just get downvoted so low that nobody's likely to see my eloquent and carefully-worded rebuttal anyway.

Perhaps an additional feature to explicitly mark your post as "rebuttal"? Then only the non-rebuttals would inherit the downvote?

And why would users not simply mark all of their posts as rebuttals? There'd be no downside.

Because rebutting something that was subsequently upvoted would incur a downvote!