I have to reread it in detail. I am too tired to make most of the equations but I got the idea.
I am just wondering, did you take in account that users will try to get the set of witnesses that maximise their profit?
On a more game theory side, every witness giving dividend seems like a natural equilibrium. It also might be viable with offer and demand dictating how the witnesses redistribute their reward.
All in all, I feel like DPOS impose witnesses to become big players like companies in the long run. Just look at what EOS will look like from the start. Still, this give a better first level of decentralization compare to PoW mining pools. If you look at the second level though, this is not good because we don't have staking pool on DPOS... yet.
I might be spouting nonsense since I am so tired so expect a more detailed/better comment sometimes later.