<p><strong>Yes. Encourage we should and encourage we do.</strong></p>
<p>In fact, StackExchange encourages it automatically: see <a href="https://meta.stackexchange.com/questions/135">Encouraging people to explain downvotes</a> Meta.SE post from 2009 that was status-completed in 2015. Users with rep below 2k get <code>Please consider adding a comment if you think this post can be improved</code> popup when downvoting - but apparently only once, whenever they downvote for the first time.</p>
<p>There is a broad consensus among our high-rep users that leaving a comment when downvoting is a good thing:</p>
<blockquote>
<p>Needless to say, like everyone else I would urge people to leave a comment when down-voting, almost always (<a href="https://stats.meta.stackexchange.com/questions/333/should-we-encourage-downvoters-to-leave-a-comment-for-their-downvote/4538?noredirect=1#comment11847_4537">@Scortchi</a>)</p>
<p>If you can say that you always comment if and when you downvote, then I admire that [...] (<a href="https://stats.meta.stackexchange.com/questions/333/should-we-encourage-downvoters-to-leave-a-comment-for-their-downvote/4538?noredirect=1#comment11844_333">@NickCox</a>)</p>
<p>Downvotes are inherently negative. They create bad feelings. Use them when they can have the constructive effect of encouraging a poster to improve a particular post. This implies that most downvotes are wasted if they are not accompanied by an effective, actionable comment. (There are exceptions: some posts are so obviously poor that little needs to be said.) (<a href="https://stats.meta.stackexchange.com/a/4522/17230">@whuber</a>)</p>
</blockquote>
<p>There is no way we can technically <em>force</em> people to leave a comment, and there are compelling arguments that this would be a bad thing anyway. Sometimes posts are just too bad and life is too short to leave a comment. But one should aim at leaving a comment whenever there is any hope that the post might get improved, or whenever there is hope that the comment might at least be useful for future readers.</p>
