I know this will be disappointing, but no, I think it would be a big mistake to introduce such a rule (that is, to outlaw downvoting for disagreement and say that people must comment instead). The site would be swamped by an avalanche of petty disagreements.
Our goal is to optimize HN for intellectual curiosity, which requires a higher signal/noise ratio. Downvotes dampen low-value comments. I know downvotes do bad things too, but that's the good thing they do, and it's big. Taking that away and/or increasing the noise with a flood of people disagreeing about their disagreements would not be an optimization.
Downvoting does gets used as an outlet for undesirable behaviors, but it's a non sequitur to blame that on downvoting. Those undesirable behaviors are sadly inevitable and will make use of any tool at hand. In my view they do less damage via downvotes than they would otherwise.
A recurring theme in the Perennial Downvote Debate is the idea of having a site where everyone presents their disagreements rationally. That's sadly not possible on the public internet—not even close—so we're not going to risk HN on trying to create it. What we will do is keep looking for incremental improvements. We've found a few (e.g. vouching) in the last couple years, and there are probably more to be found.
Edit: this later comment is relevant here: https://news.ycombinator.com/item?id=16131314