being fully honest, i have simply dont understand what your saying, maybe my view is too high level. to me you either prove you computing power (POW) or you prove your economic power ( POS)
i think we'd need a face to face discussion with a blackboard to understand your point.
Do you understand that the act of mining itself is technically a decentralized exchange? Most people don't know Bitcoin has a decentralized exchange, but that's exactly what it is. It's a permanent decentralized exchange because the block reward is subsidized by transaction fees so you can always go straight to the tree itself to pluck off coins. If you remove this peg, it becomes a closed entropy system and is no longer decentralized, but only a distributed, permissioned ledger.
Bullshit, an exchange is a place you can buy and sell stuff. You can't sell bitcoins by mining.
Mining is a way of obtaining bitcoin that doesn't require authentication, but that's about it.....