The CPU of one individual person wouldn’t compete with anyone.
The idea is that gamers/users could basically sell the small power they generates with their computer to the ETH network and receive a small amount of gwei through a dapp. They would only be able to keep a small portio of those gwei, basically get paid small amounts to play games/use electricity, by selling power credit to the network, so it can be used it to pay miners (not sure if this is possible. But this forum probably a good place to check)
The rest of the gwei the app receives would then be sent into a pool on the ETH network that would basically help pay the miners and be less taxing on the individual making a Tx.
Example: Few hundred kids are playing fortnite on their CPU at home at the same time, all getting gwei for the kW they use via this hypothetical dapp. This dapp sends most of the gwei they generated to this pool on the network. At around the same time, you’re on uniswap about to be charged 100$ in gas fees. But then the EVM checks to see how much it is able to take out of that pool to help you with those fees, based on how much is in the pool and how many Tx are happening at that time. Your gas fees are now 36$. Miner gets paid the same. Unused ETH in that pool must eventually be burned as to not create too many coin and bring down the value.
Anyway. This is just an idea that came to me and even if valid, would be a very complex balancing act. I was just curious to see if it was possible and thought would be interesting to read the answers.