I think that will be muggy as heck.
It doesn't look like fresh air has an easy way in at all.
Also if it is that closed down cut the inner wall to a mesh skirt to save the weight.
Also the fly will sag and will need pullout in the middle of the panel (like a ray-way tarp) to pull it up away from the inner/your face.
Your original idea has more merit in my mind as with a tarp overhead you will still get moving air which can cool you, dry gear, cut condensation and move your stink away, FAR AWAY.
The fly doesn't have to surround the bug shelter, that's just a tent and for me there are many reasons i quit on tents.
Obviously if intended for extreme wind and cold then your current setup is better than a floating tarp overhead, but if using it in hot windless areas you'll want as much airflow as possible.
I wouldn't mind it if i were wrong, if others have opinions that differ from mine please share.