Honestly, letter of intents (LoI) do not affect the program ranking list.

If it really did, everyone would be sending #1 LoIs to every single places they interviewed at by now.

Don't assume that people are gonna be honest. Last year, there were even cheaters who were invalidated. I assume it won't be hard to find dishonest people spamming their #1 LoIs if LoIs did have critical impact.