Damage Cooldown can negate fall damage

I can only reproduce with the exact combination of fire and fall damage

Also noticeable in mob kill traps, they take their fall damage and then .5 sec later trident kills them.

That does not happens only when you are on fire. Trident killers, you know, are always used to kill mobs automatically. However, if you combine it with falling damage, sometimes trident don't hurt mobs when falling damage is hurting the mob.

The easiest way to replicate this is to damage yourself as you're still falling (at around 12 blocks or less from impact)

Spamming end crystals on the ground while wearing full diamond armor after eating an enchanted golden apple (which gives regeneration 5 for 30 seconds) will negate explosion damage also. When giving myself health boost and spawning about 40 husks around me, they not only didn't do any damage, they didn't knock me back either. Therefore, it's safe to say that that the cooldown can negate many types of damage, not just fall damage. 

When testing this the other way around, by giving a villager just regeneration 5 (to simulate a player eating an enchanted golden apple during a fight), it is also impossible for players to damage others that are healing.

Still affects 1.18.12, however sometimes in multiplayer for some reason sometimes players don't take any fall damage at all do too lag or something else

This was probably fixed in 1.18.30 with the overhaul of damage calculations. I cannot reproduce this in 1.19.51 Hotfix by falling while on fire or by falling while hugging a very tall cactus.

The reproduction steps in the description seem to be misleading, however, because I don't ever take fall damage from hitting the bottom of the void, regardless of the timing of void damage.