Just remember that on here LOI could mean letter of intent or letter of interest -and those are very different things.
I personally think for a letter of intent, when to send it depends on the likelihood of a rejection. If the school only really sends WLs and no post-II Rs than it’s probably better to send it earlier because once you’re waitlisted and so are the other 500 people they interviewed — the school will likely get a surplus of letters of intent and they will mean less/hold less power. If they do send rejections, better to send pre-decision if you think you’re a weaker candidate and post-WL decision if you’re a stronger candidate. If you’re a weaker candidate, you may be more likely to get rejected outright and not be put on a waitlist. If you’re a stronger candidate, sending a letter of intent too early can hurt your chances at merit scholarships. If the school has had no waitlist movement in past years, better to send now because a waitlist basically means a rejection. Also depends on when the school begins reviewing your app post-interview and making an admissions decision (I know Hopkins reviews them almost a month before decisions are sent out so anything sent in the month leading to their decision may not even be viewed or weighed in their original decision, don’t know about Cornell though).
There’s a lot of other factors I’m not weighing as well, just my opinion.