I believe that adding downvote option to the LQ queue would do more harm than good.
This will likely be unpopular opinion among experienced reviewers, and for a good reason - being one of them myself I would much benefit of this option (see note at the bottom of the answer). But thinking of less experienced reviewers makes me feel like this isn't the way to go.
Main problem with providing downvote option in LQ review is an obscure, counter-intuitive possibility of an unexpected reputation loss.
Just think of it. Imagine an average, moderately experienced user just over 2K reputation doing LQ review. Imagine them looking at apparently poor quality answer shown under big bad title "Low Quality Posts", heavily voted down, having comments clearly explaining what's wrong with it. Many of them will probably pick that vote down option because it is so apparently correct one.
Now, how would they feel like after it turns out that review didn't delete the answer? (1, 2, 3, 4)
- Hey what's up, I did nothing but few LQ reviews and now I'm out of 20 rep points?
- Oh that's all your fault: these answers weren't poor enough to merit deletion because of <some intricate obscure formal reason>.
Would you expect a user penalised this way continue reviewing? Hardly. Would such a penalising be fair? Why would it?
We're talking about average users with typically limited experience. They come here to just ask questions and get answers, "...no distractions" as they were promised in tour. They are not obliged to distract (yes, distract) on studying complicated nuances of when an answer is poor enough for downvote but not enough for deletion.
The reasons why we ask these less experienced users to review is because we can't do without them, because other ways we tried didn't scale. Diamond moderators couldn't handle it, 10K users couldn't do it either, so we asked these less experienced folks for help in maintaining site quality.
But we can't expect of them same level of understanding as that of 10Kers. And we can't really afford repelling them from review because of unexpected rep losses - because we already tried and found that without them system doesn't work.
Summing up, if we want LQ queue to work and scale successfully we better keep the downvote option out of it - because this tempting and obscure "rep-eater" would likely be a permanent drag-off for less experienced reviewers.
(For the sake of completeness, I can think of providing it as sort of advanced option for users with over 10k rep or maybe over 1K reviews - but not for less experienced ones, that's for sure.)
A promised explanation why to me personally this option would be very convenient. Myself, I vote down lots of posts from LQ queue and it sure would be much smoother if I could do this without opening them separately.
It is critical here that I fully understand rep-implications of my votes. I know when there is a risk (reviewers can disagree to delete and I won't have reasons to flag for moderator) and I fully accept that risk of rep loss. I also know when there's no risk - even if review breaks or author undeletes I would flag for moderator and get it deleted anyway.
But this all is based on higher than average understanding of how system works, and I got it only because I was personally curious about that and I can not expect other reviewers to be just as curious - simply because they are not obliged to and they have a full right not to bother. I don't want them to lose rep essentially because they were simply not as curious as me.