IMO serrations are simply meant to be a way to extend the cutting ability of a knife without sharpening it, that's really all there is to it. So, take two identical knives in a low grade soft steel, one serrated, on plain edge, start with two sharp knives and start cutting cardboard. You will still be able to "saw" through the cardboard with the serrated blade long after the plain edge is useless, so for the majority of casual users, serrations will allow their knife to remain useful for longer, while also being able to be made with a lower end steel that allows the price point to be more attractive to that same casual user. This also explains why serrations are so
unpopular with the hardcore knife crowd, we keep our knives sharp and will pay for the premium steels that allow them to stay sharp even through extended use.
EDIT: I do have to agree with kage, first responders dealing with seat belts are an exception. They need to quickly cut a strong synthetic material with possibly very little leverage and a bad angle and it needs to cut quickly and reliably, so a full serrated sheepsfoot is the way to go.