I don't really understand how a mining-less system can function either. I mean, sure, right now most of the income from Bitcoin mining is from newly minted coins, but as the number of coins minted decreases the usability as a currency should be increasing which will lead to a gradual shift towards income from transaction fees. In fact, Satoshi probably predicted the move towards mining hardware at ever increasing speeds so that by the time people stop making money from the minting their machines are able to process enough transactions to actually allow the transaction fees to go even lower and work even faster at equivalent ROI to the minting of today.

In a mining-less system the income is exclusively from minted coins without any strategy for the shift towards transaction fee income. There is even this interesting concept called "Proof of Burn" which although presents an interesting low energy cost approach to distributing new coins has not even considered the role hardware has to take in maintaining the network. In either Stake or Burn the focus gets shifted away from the hardware that holds everything together. Even in the better stake proposals that allows people to be rewarded from mining alone, the fact that people are rewarded just by holding coins would seriously disrupt the expansion of the network which would be required for it to become the world reserve currency for all transactions everywhere.

In the worst case scenario, based on fluctuating price, energy, and hardware the rewards for holds could become higher than mines which could in turn result in a rapid shut down of mining hardware to the point that the network ceases to function fully or at all. Sure, the existing mines won't shut down right away, but as people stop investing in new mines and stop buying more energy efficient hardware as energy prices go up the old hardware could be gradually decommissioned without replacement. That would be a consequence of the BETTER proposal where you are allowed to earn from mining independently of holding. In the other scenario where you have to hold and mine it would guarantee that only the wealthiest control Bitcoin, but more importantly would cut the network expansion rate in half which would seriously compromise required network growth.

The emphasis needs to remain with proof of work because that is the only model that will allow the network to expand as it must while providing the required buffer to keep everything working in the event of price declines as will occasionally happen.