From a miner’s perspective fee is payment for an increased uncle risk, so decreasing the total received fee must lead to reduced capacity, assuming rational miners.
For this reason the minimum fee system would increase volatility of fees and reduce throughput, as fees would have to be the same as they are currently on top off minimum fee. It’s a dynamic tax creating a deadweight loss.
Fees are volatile because high fees don’t increase the gas limit, ie. ‘high’ fees are too low relative to the block reward. The moment fees attain level high enough to buy additional block space the market would stabilize and become predictable.
The simplest solution is to reduce the block reward, which has separate security considerations.
A weird one would be to allow miners to gift a portion of their rewards to future blocks, paying future miners to not orphan them.
A hybrid PoS/PoW with PoW chain for validator selection/joins/exist and PoS for block generation would also work.
Fee as a function of time and/or block height is a very good idea, although hypothetically it could incentivize intentional orphaning. The difference is that the current way of replacing transactions hides future pricing information.