Not sure what you mean by equal mining power. So a guy with one card would be able to mine as much as a guy with 10 cards? That wouldn't be profitable for the second guy?
Exactly. In fact, no cards are needed. No POW at all.. but you can mine it as if you had equal hash rate as everyone else mining. You instead use your digital ID as if it were a miner and every block the person with the best digital ID for a given block number wins. Some randomization involved.
So it's like every block either you have the winning hash or not and you can't just try another hash.
Well, that will not be mining then but it will be more like Airdropping or just a distribution that occurs every set amount of time. If you want it to be more like mining then you can set a virtual mining process that gives everyone an equal hash rate but needs a user to be logged in to get the hash set for him, this is just a suggestion.
Not exactly, they still need to process transactions for our blockchain(s) in order to earn rewards. It's mining in the sense that Proof of Stake staking is mining.
Can you think of a better way to easily and quickly express this idea?