Benefit of eliminating mining pools?

[xeroc]

Overall hashpower will be lower without pool mining.

More energy is waste if you don't have a pool. Simply because hardware potentially derives hashes that have been derived earlier by another miner

That isn't true, every user is generating a unique sequence because their key is factored into the hash, no two miners ever generate the same hashes.

I came to the same conclusion thinking about it more closely.

[monsterer]

Overall hashpower will be lower without pool mining.

More energy is waste if you don't have a pool. Simply because hardware potentially derives hashes that have been derived earlier by another miner

Only true if orphaned blocks don't contribute anything.

[Empirical1.2]

Mining pools promote centralization of block production, but decentralization of hashing power.

What about a coin with subsidized P2P pool? https://en.bitcoin.it/wiki/P2Pool

Decentralized payout pooling solves the problem of centralized mining pools degrading the decentralization of Bitcoin and avoids the risk of hard to detect theft by pool operators.

I don't understand mining very well but with a subsidized P2P pool couldn't hashers get the benefit of the much lower variance they get from a centralized pool but with a slightly higher reward while the network gets the benefit of reducing the centralization of block production?

[bytemaster]

Overall hashpower will be lower without pool mining.

More energy is waste if you don't have a pool. Simply because hardware potentially derives hashes that have been derived earlier by another miner

That isn't true, every user is generating a unique sequence because their key is factored into the hash, no two miners ever generate the same hashes.

[xeroc]

Overall hashpower will be lower without pool mining.

More energy is waste if you don't have a pool. Simply because hardware potentially derives hashes that have been derived earlier by another miner

[bytemaster]

Mining pools promote centralization of block production, but decentralization of hashing power.

A system without mining pools would be dominated by large solo miners and smaller miners would be unable to participate at all.

Overall hashpower will be lower without pool mining.

Number of block producers would be greater (better censorship resistance).

Others?

[sittingduck]

Ignoring the problems with mining in general... Which is better: a coin that is mining pool proof or one that supports pools? 

Why?