I applaud your enthusiasm, and agree that as many questions as possible should have good answers, but ... it's easier than you might think to lose track of quality in pursuit of quantity.
Please don't be too discouraged by the following answer. It's great that you're keen to help improve the site, and solving unanswered questions is a very worthy goal, but we need to be very careful about how we go about organising such an effort, to avoid making the problem even worse than it is already.
Back in private beta, there was a huge surge of new questions and answers in the very first few days. Many of the answers provided back then were very low-effort (e.g. comprising not much more than a quote from Wikipedia or Shmoop) and yet still stand to this day with far more upvotes than they deserve. We've got much (
much) better at writing high-quality answers and voting down low-quality ones - partly due to shifts in the userbase, partly due to existing users learning and improving - but there's still a danger that seeking an answer just for the sake of having
an answer might distract us from ensuring it's a
good answer.
If you can't answer it well, don't answer it at all. That sounds a bit too strong, but really, the last thing we need is more bad answers knocking around. It's much better to spend a few hours writing up a really good answer to one question than to spend the same time posting mediocre answers to ten unanswered questions. None of us can answer everything, so let's try to focus on what we can.
Remember to downvote as well as upvote. It's important to mark good answers by upvoting them, yes ... but it's equally important, nay, more important, to mark bad ones by downvoting them. People are very unlikely to spend rep downvoting good answers, but they can and do upvote bad answers, and wanting to reduce the number of questions marked as Unanswered just provides extra motivation.
Don't focus too much on statistics. Answer quality can't be judged objectively by figures, least of all on a site like this. Our main objective should not be to reduce the percentage of unanswered questions, because we could achieve that by posting and upvoting bad answers. I know that's not at all what you're advocating, but if you make "getting questions answered" the primary objective, people will start doing that, just for the buzz of seeing those numbers decrease. Imagine this situation:
Here's a question which I'm not competent to answer perfectly, with an existing zero-score answer which isn't all that great. Should I leave it alone in the hope that someone will eventually answer it better, or should I upvote the answer because YAY, another post knocked off the Unanswered list?
We know what should be done here. But we also know what would feel more satisfying to do.
Patience, my young padawan. This is what I always say to people too obsessed with reputation or badges, and really, much of the same reasoning applies here. Getting rep shouldn't be a goal in itself; focus on providing good content, and the rep will flow in anyway. Same here. The numbers shouldn't be our priority; focus on providing good content and they'll sort themselves out automatically.
Finally, remember that unanswered questions are easy to find. An expert in Author McPoetface can join the site, look for unanswered author-mcpoetface questions, and put their knowledge to good use in answering them. If they already have upvoted subpar answers, then a) they won't appear on the unanswered list, and b) experts might be put off from providing better ones. A question poorly answered is actually worse for the site than one not answered at all, which makes it even more important for us not to post answers just for the sake of posting answers, but focus on quality.
Here's how this can work.
Maybe all of the above was a bit dampening to your spirits and enthusiasm. Sorry about that, but it did have to be said. Here's a (true!) story of how what you propose can work in practice.
- Earlier today I was browsing through the unanswered poetry questions, looking for something to answer, when I found this question about the poem "A German Requiem". Over the next several hours, I read the poem many times trying to understand what it was all about, read existing analysis and critique of it online to improve my understanding, looked at all the three questions about it on the site so far and the single existing answer to one of them, and gradually built up my experience until I was ready to attempt an answer. I was lucky enough to have stumbled across a poem with two unanswered questions about it, so I managed to knock two off the list. The majority of my SE time today has gone on researching and writing those two answers.
If people are willing to put that kind of effort into answering old unanswered questions, then maybe this can work. But the goal should always be to provide answers we can be really proud of, not to make the numbers go down. If we start worrying too much about numbers, quality could suffer.