Two problems that two-handed rods solve: 1. It's less tiring to cast a two-handed fly rod than a one-handed one. (True, with a 3- or 4-weight this isn't as big an issue.) 2. Using a two-handed fly rod requires less back cast room, and therefore we don't have to wade far out in deep/fast water. (This is why spey rods were invented in Scotland many moons ago.)
Randy