This smells like a dupe -- but it does have a minor variation, so I'm keeping my close question trigger finger safely under control.
In addition to the reasons others have mentioned (like retaliatory downvotes -- and, BTW, Jon Skeet got a serial downvoter just today), there's another aspect to this. You ask:
What do you think about requiring that the down-voter possess a certain level of rep before being able to downvote questions without also leaving a coment?
You go on to suggest it should be the edit rights boundary. We already have a minimum rep before you can downvote at all; admittedly a low one (100 rep). Why should people with under 2,000 rep have to explain or even just reveal their votes, potentially subjecting them to retaliatory strikes? They have the right to their opinion, too. Under this scenario, if I downvote something on SU or SF, I have to explain myself. Why? Is my opinion inherently invalid because Arbitrary Numbering System says so?
We might disagree with it, but if you do, you have the power to right the wrong: Click the upvote button if you really think the downvoted post was right, correct and useful. (Or in the case of a question, useful, interesting or otherwise upvote worthy.)
However, please don't "sympathy" upvote, where you upvote the post just because it got a downvote. Upvotes outweight downvotes by (currently) a factor of 5 -- there's simply no reason to sympathy upvote. Ever. Upvote because you feel it truly deserves it, regardless of its current score.
Anyway, many of us on Meta would argue that there's not enough downvoting. You think I take every one of my downvotes personally? Lord, no; I'd be too busy crying over my arbitrary number to do anything worthwhile (on the sites or in my life)!