What does the hose that goes from top of the thermostat housing down to a crossover do? I've seen some setups with it and some without so I was curious as to what it does and/or the benefit?

It allows water to flow through the exhaust while the stat is closed. Usually there are 3 or 4 small holes drilled in the stat flange to keep the temps even when it is closed, but they do not flow enough to keep the headers cool.
Hope that helps.
Dick

Indeed it does help and makes sense. Thanks for the info.