A serrated sword seems like it would be better than a regular sword, as it would be able to inflict deeper cuts, and potentially hook enemy swords, giving the wielder an advantage if they are stronger. Despite all of this, in nearly every depiction of history, they are virtually never seen. Is there a reason for this, and if so, why?
The simple reason is that actually a serrated edge is not better for chopping and it won't inflict deeper cuts. You can saw through things better with a serrated edge but in combat you don't have time to do that, and a smooth edge will penetrate much deeper in a single strike than a than a serrated one will. A serrated edge is actually terrible for chopping because it won't get through a surface "cleanly" and it will easily get caught and tangled in clothing and things like that. That's why axes and large butcher knives meant for chopping are never serrated. The only time a serrated edge is useful is when you're able to do a systematic back and forth sawing motion on whatever you're cutting, which is rarely useful for combat. The closest swords have really ever come to serration is when the blade is slightly wavy such as in the Southeast Asian kris and some European Landsknecht swords, but that's not a fine serration at all, although it could potentially aid a little bit in some slicing actions by concentrating force in specific parts of the cutting edge.