Serrated edges does not cut better, actually they cut worse. They saw better, but in combat you don’t have the time for sawing through anything.
You can try yourself with two knives of similar mass and weight distribution, one serrated and one properly sharpened (be careful though).
Surely you can kill someone with a serrated blade but it's still harder.
And surely you can inflict fringed wounds (which are worse to heal but not really more deadly for short term periods), but your weapon it's going to stack everywhere, making that quite dangerous for you unless it's a throwable weapon like arrows and javelin.
Against cloth armours like gambesons a serrated blade it’s really a bad choice because it will almost always remain stuck and will probably not cause a lot of damage anyway in the process of remaining stuck.
A serrated blade would actually be a little better against plate metal armour because it should bind better instead of glancing, transferring more blunt force. But the majority of bladed weapons like sword doesn't have enough mass on the tip for being useful as blunt weapon no matter if normally sharpened or serrated, that's why in late middle age martial art has being developed the mordhau technique for combat in armour, which consist in grabbing the sword by the blade and use the guard and pommel as the head of a mace/warhammer.
Maibe an axe (or a falcata) can benefit by serration against plate metal armours, but a mace or warhammer would still be a lot better for this task, and a normal axe would be better against flesh and fabric armours (A lot of medieval pole weapons had 2 separated heads: an axe and an hammer)
So there are no reasons for it.
Deep serrations has been used in parrying daggers, commonly known as “sword breaker” (a term that should be substituted by “sword catcher” since it's almost impossible to break even a low quality sword that way, at the very most you can bent it since it’s metal not ceramic), you can't put such protruding serrations on a longer blade without making it too weak or too heavy, and you don't want to use it alone but always with another weapon because if you catch your opponent blade then your parrying dagger is also stuck and not usable for offending.
So what else? Maybe trust/bind oriented swords
We have established that serrations are actually useful on blunt weapons (not edged), parrying weapons and missiles.
What about bladed offensive weapons?
We have said that serration decrement the cutting power so we have to exclude more cut oriented weapons like sabres/scimitars.
It's probable that even a shallow serration would increase the friction between two blade during a bind, allowing for better controlling your opponent’s blade (but I don't know if it's sensibly better than a normal proper sharped blade for practical purposes).
So maybe we can use it for defensive purposes (not offensive) in trust oriented weapons that are used in a martial art focused on bindings like in HEMA, such weapon can be the rapier.
Rapier can also cut but its usage was heavily trust oriented as opposed to their predecessors like sideswords and armingswords, which also tend to prefer trust over cut but to a less extend. Rapier also eventually evolved in smallsword that was completely blunt due to its triangular section.
So i assume putting serration on a rapier shouldn't really decrease by much its offensive effectiveness, maibe would be better to leave the weak of the blade normally sharpened since you don’t want to parry with it anyway and you will use it for small quick cuts.
Putting serration on blunt swords like smallsword and estoc don't detract noting but also don't add nothing usable in the context those weapons were used (the first was a duelling sword and the second specialized for fighting in armour).
Also actually a good serration that is sensible better for bind control and dont weak the blade can potentially be puted on the strong of the true edge and on strong and medium of the false edge of basically every sword without actually impair their cutting capabilities for practical use in combat, at the same time improving a bit the parring effectiveness since you want to parry with the strong and cut with the medium and weak.
Anyway I have historical records of serration only on the false edge of more recent swords used more like a tool/weapon hybrid.
Probably it’s not that much of an improvement for combat compared to crafting, maintenance and tradition issues.
Sources: I'm an hema practitioner and enthusiast, and i follow different related youtube channels and blogs. I suggest Scholagladiatoria and Shadiversity over others.
For what concern claws and teeths they are not meant for slicing but for trapping the prey.
Even if nature can create something sharp like a sword there’s nothing in common between how an animal use its jaws and how we use a saw or a sword.
With saws and swords you make forward-back movements in order to slice, with jaws you crush things opening and closing or rip flesh keeping close and pulling with movement of the head.