I think what
@Goro is trying to say is that, even for needy schools that encourage grovelling, including meaningful updates that make you more attractive as a candidate is likely to have more impact than a simple begging love letter.
In the end, everyone who bothered to apply, pay the secondary fee and attend the interview has a high level of "interest," and a decision (especially at a highly ranked school like WUSTL) is unlikely to be swayed by who has the creative writing skills to write the most moving love letter to the adcom. That said, if they are openly soliciting them, you do run the risk of hurting yourself if you don't play the game.
For undergrad, I was placed on a few WLs, and while I expressed interest through portals to remain on the WLs, I didn't write any love letters because I already had several excellent choices, and wasn't super interested in begging schools where I wasn't good enough to receive an initial A when, other, equally good schools, did want me in the first go around. Not sure if it's the reason why (and, to this day, don't care
🙂), but I wasn't called off any of the WLs!!!