Solo miner hash rates do not sum.
Why not? Every single miner, who is working on the heaviest chain, is raising the difficulty. No matter, if it is solo miner, or some miner in a pool. And even Merged Mining is counted here. You can mine NameCoin, RSK, or whatever, but if you produce valid Bitcoin blocks as a part of the process, then you still contribute to the total network hashrate.
More than that: if you mine an altcoin, which just blindly follows the heaviest chain of Proof of Work (no matter if it is valid or not), and where you receive amounts, proportional to your hashrate, then you can even reach de-facto 1:1 peg with Bitcoin, if you do that properly. Why? Because then, the cost of mining 1 ALT, will be equal to the cost of mining 1 BTC (no matter if you produce one satoshi every 10 minutes, or if you produce blocks every 30 seconds like P2Pool did). And if your peg will be enforced with signatures, and no coins will be created out of thin air, then it will be de-facto 1:1 peg.
and all but one loses, resulting in an extraordinary waste of energy
You know, what is "share"? It is
invalid block, but miners are paid for them anyway in centralized pools. Which also means, that it is possible to collect all of them, and sum them up on a separate chain, and then push that batched transaction into Bitcoin.
The only problem with centralized pools is that they are, well, centralized. But there are ways to do that in a decentralized way. And also, putting all miners in one basket is not strictly necessary. You can as well sell your shares in Lightning Network, and receive cheaper transactions, according to your hashrate. In this way, it could be possible to send free transactions in LN, if you are a small miner, and if you mine single satoshis or millisatoshis. In that case, it makes no sense to make a new on-chain transaction, because even the minimal fee can be bigger than the amount you earn by mining.
And also note that if this model will be more popular, then finally, some of those miners could produce some valid on-chain block, which will include their own free on-chain transactions, needed for payments, channel management, and so on.
No, the mining pool would have the higher hash rate because their hash rates sum and that contributes more difficult blocks.
Wrong. You can compare P2Pool total chainwork with the main network total chainwork. The more shares you collect, the bigger your chainwork will be. And of course, P2Pool is a proof, that it doesn't have to be centralized.