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.
If you want to use the system, you require native tokens, and in a closed entropy system, you're at the mercy of whoever owns them to extort you. In Bitcoin, it's an open-entropy, permissionless ledger, so this is not the case. This means the only way you could actually define closed entropy systems is basically companies or businesses. The nash equilibrium is then lost for much of their use case.