Right now there are 31,017 first posts by new users that need review, 2,797 of which have been reviewed in all time.
The new /review queues are, well, new. Do you have any evidence that its size has been increasing at an alarming rate? And for the record, the close queue is nearly twice as large.
I think that more and new incentives are needed so that we can get this number down. There are over 696,098 reviews for suggested edits and 139,811 for low quality posts so there are definitely enough reviewers.
Yes, there are enough reviewers, and there's no incentive on the other reviews, so why would there need to be one on this? Just because it's not getting the same attention isn't a reason to incentivize it, figure out why it's not getting the same attention and we'll see about remedying that more directly.
If SO implemented something like 2 reputation for each review, a banner ad on the home page and a blog post then we could probably get the number down to zero. And, once it's there it'll probably stay down.
And we'd get a lot of people just clicking through, doing no good and potentially harm beyond just removing it from the queue for people who would help, just for their free rep. Bad idea.
The other solution could be to remove everything older than 2 weeks and anything with an answer (they are obviously questions and readable).
I think Anna addressed this well enough. Just because it has an answer doesn't mean it's a good (or even acceptable) post. And we shouldn't just let new users or bad posts fall by the wayside just because they're getting older.