Seems to me that formal studies would have more of an effect looking at how to manage crowds that are already too dense without making things worse. If you want to avoid the density in the first place, you decide on a maximum density within a central perimeter, and also manage density appropriately along the ingress routes. That way you don't just push the unsafe densities into the outer side of the perimeter. And you set your desired densities low enough to both avoid dangerous situations inside the central perimeter, and allow the central crowd to get out if there is a fire/etc. inside it.

Essentially if you want a max density in area A, you enforce some other max densities in the area several times larger than A.