Not so sure about that when you consider levers and who has the short end of the stick. Now, a longer fighting butt would give you a little extra leverage.
You're right, leverage was the wrong term. You give the fish more mechanical advantage. i.e. you have to apply more force to the rod to apply the same force to the fish.
I still stand by, though, that it helps you fight the fish with a longer rod. Otherwise, NO rod would be the easiest way to fight a fish. For us, even on steelies on a long rod, applying more force is not a problem, we have more than enough force available. In fact, the only reason we don't apply more force than we do is so that the tippet doesn't break. It's not us vs. fish. It's our tippet vs. the fish, and we're trying to manage it so that the tippet wins.
We have a distance advantage, i.e. we have to apply that force over a smaller distance than the fish. Our goal is to provide a constant and steady pressure, through all the runs and headshakes that the fish throws at us. A longer rod helps with that. When he comes towards us by 3 ft, we can pull back the rod only a few inches and keep the same pressure. The larger bend in the rod also helps steady the pressure by absorbing the variations.
You do notice, with heavy saltwater gear meant for big tuna, billfish, and the like, you see shorter rods, with higher handle holds.