They control the gap along the fender and hood while driving. On some earlier cars you can lean on the front of the fender and see the gap change a little bit along the hood. I've seen a few Mopars that has chips in the paint where the hood got closed and didn't have enough gap.
It's my understanding that the later cars had thinner sheet metal and thus needed a little extra bracing.
They offer nothing for handling or chassis rigidity. Body rigidity only.
I have a set I'd sell if you're looking em.
