Why?
All they really do is add a bit of drag and act as an air brake. Please make me aware of what I'm over looking here.
*sigh*
It is produces a constantly shifting force vector as it buffets in the turbulent air.
It is largely static in force produced and not variable like the fins.
It will be redundant as the body and fins are already sufficient aerobraking surfaces.
It will act as a large sail for wind causing the craft to roll and translate unpredictably.
It will consume a significant mass fraction in order to be large enough for a vessel of this size.
It will require its own complex deployment system with pyros and mortars to deploy it eating up more mass.
It will be dead weight during most of the mission not providing any ancillary ability (heat radiators in the fins).
...
And that's just what my kerbal flinging amateur rocketry nerd self can come up with. Imagine SpaceX's list of why they chose no chutes.
So, NO PARACHUTES, capiche?