Frank my intuition (that means I don't know shit what I'm talking about

) tells me that a larger chute (less impact) would take more time to deploy. That means it would have to be usable in a higher altitude and that defeats the idea of the chute as a safety measure.
More thought.. You get into a spin and you have no altitude left to recover. You open the parachute.. These situations are more or less the what is on the mind of those who develop those chutes. So, you see, minimum altitude to deploy is a big factor.
Some of the others who work with "paratroopers

" can perhaps shed more light to your question.. I believe that the second, safety parachute the jumpers have behaves much the same.