Personally I think she's too high on the list, a character with such a predictable recovery, laggy moves, light weight, annoyingly precise aerials and terrible offstage game/approaches shouldn't be that high lol.
Predictable recovery... yeah, how many characters who aren't top or high have unpredictable recoveries again? They generally have other alternatives, but looking at that list, the only one I probably couldn't guess with relative ease is ZSS. The rest can recover in different ways, but they're not unpredictable. I'm not saying Zelda has omg amazing recovery (she certainly does not), but her recovery being predictable obviously doesn't hurt her that much, and if it does, it hurts everyone else evenly.
Laggy moves... perhaps. That said, there aren't really any characters below her who don't have laggy moves elsewhere. She does have quite a few, but they're obviously not so laggy that they become use-it-once-per-match-esque. For those with a laggy moveset, they have to use most of their moves anyway, and again, I don't see why this should knock her down if others lag like her, too.
Weight is one of the smaller factors to consider. Yes, yes, I know that MK being light doesn't hurt him too much because he has all sorts of other things to make up for it, but out of the things you listed, weight is, in my opinion, very trivial. It's not like she's Jigglypuff and doesn't have much of anything to make up for it.
Precise aerials would be correct, but hey, if you're playing at a serious level with someone who has precision involved, you're obviously going to become skilled at landing said moves. Practice is all it takes to help out your own kicking game; getting to land the things on competent players is, admittedly, not the easiest thing to do. Perhaps her preciseness kept her from rising so far up in the first place, along with other lame things about her. If that's the case, I don't think they should dock her any more points for it.
Terrible approaches/offstage, relatively speaking for the most part, would be correct. That said, she has other things to make up for it, and apparently those things that compensate for her approaching issues are better than others who have the same issue but can't make up for it as well. (lolLucas, who also has a better recovery, generally better tilts, and does better at forcing an approach... but still places Low)
I don't see why she shouldn't be where she is. Her match-ups in general are not terrible, and if she loses out to someone, they're usually top/high already (save perhaps Lucas, Olimar, and apparently, Peach, and Oli is above Zelda anyway). She also has other perks, like being one of the few characters who actually gives Falco a hard time (as she doesn't get chaingrabbed, which is already one of the big main things about her here), being effective vs. D3 thanks to his size to alleviate her aerial precision issues, having the power to off him, being able to intercept his recovery for a kill a bit easier than most, and not getting chaingrabbed again, being able to match up with Robot (I assume that it's even, since Sheik/Zelda > Robot, not alone), and (currently) running even or better with all of high tier save Marth. Yeah, she has her glaring issues which I'm sure you and I both know of, but honestly, why is she too high? Where are you putting her?