Why X essays don't matter. Period. You're in or you're not in.
Not really. I would say they matter if you're borderline and/or if you can come across as genuinely interested in being at the LS. However, it's also that they probably won't make much of a difference if you're above the median numbers. Also, you might want to note that I am talking about >T14 schools here. I don't know much about the top schools, esp. YHSCCNN, to assume that above-median numbers are auto admits.
I strongly recommend writing a Why X essay if and only if you have compelling (not to mention genuine) reasons Why X.
Why X essays don't matter. Period.
If you insist they don't and don't send one AND you don't get in, then they probably do matter. If you persist and send one anyway AND get in, they probably do matter as well.
A dose of fatalism: if they are to matter, they will. If they're not going to matter, they ain't going to matter. So what the hell. Just send one anyway (i.e. iff you are genuinely interested and have compelling reasons Why X).
Sort of like Pascal's Wager, with its flaws and all.