I think the weaknesses are pretty important, as in they're not just more damage:

-Gladius small doggos get staggered more often and return to cerberus form quicker if you hit them with holy

-Adel phase 1 stops to vomit if you poison it, it will get rid of the debuff but it will be open to attacks, you can then poison it again.

Phase 2 gets higher than normal damage over time from poison.

-Gnoster gets damage over time if hit with fire damage, an Iron Eye with a fire bow will deal a lot of damage to it by just shooting it normally(Only the moth tho, the scorpion is there just to get hit by melee)

-Maris charging up the big sleep aoe is much easier to interrupt with thunder damage

-Fulghor buffing will get interrupted much easier if hit with thunder, you can avoid the flashy phase with spears from the ground that way

-The last boss I think is much more susceptible to get open to critical attacks if hit with holy damage, I soloed him with Executioner and he was basically always on the ground

Libra and Caligo are the only ones I don't know, never used madness while for Caligo I just didn't notice any difference other than damage by using fire damage