Most schools at least rank their WL people internally - at least in tiers. In the beginning of the WL season, they will likely go to the top tier and replace any given offer with a similar applicant whenever possible. As the season goes on, especially within a couple weeks of first day of school, the adcom office may be more judicious and offer any last minute spots to a known candidate. This would include a student known to already be in the area, working at the institution with a powerful PI, etc.
Most schools do not have a ranked list bc they will not be necessarily going in a pre-specified order as they offer up WL spots. In order to end up with a diverse, balanced class, when an accepted URIM female Ivy grad with strong scores and strong basic science lab experiences decides to go to BMS (best medical school!), SBMS (second-best medical school) wants to replace her with a similar WL applicant.
Of course, the schools continue to have the upper hand for most of this process. They WL many more students than they could ever imagine needing, as there is no way they want to end up with no one to give offers to. So you can be sure that the schools have very deep wait lists that far exceed the number of students they have ever needed to approach.
The lowest tier schools will be at a relative disadvantage though of course. After June 1, WL spots will be just a trickle and the vast majority of WL spots will be the result of domino effects from higher ranked schools.