(Of course, this requires a selection process that is truly random and manipulation-proof).
You are right back where you started like a dog chasing his tail and not knowing it.
Because you can't achieve that without proof-of-work, as I wrote 3 years ago:
The other attacks you describe all derive from the fundamental reason I declared all non-proof-of-work systems to be insecure back in April.
My logic was mathematically fundamental. The input entropy set is quite deterministic and well known and thus can be preimaged. For example, accumulating a lot of coin-days-destroyed and then targeting them in clever ways to subvert the security.
The randomness (entropy) of each proof-of-work is fundamental and mathematical and it can not be preimaged. It can only be surely defeated with > 50% of the network hash rate. Note I recently offered what I believe to a solution to the selfish-mining attack (the one at hackingdistributed.com that claims 25 - 35% attack).
I am skeptical that you can characterize all possible attack vectors of proof-of-stake in one coherent mathematical proof. Thus you will not know formally what the security is; instead a list of adhoc attacks and counter-measures.
Your contemplated design is essentially just Bitcoin-NG in disguise.
How did you solve this issue in your version of unprofitable PoW?
I discarded proof-of-work and formulated a consensus ordering design concept different than just proof-of-stake, DPoS, or a DAG.