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Why is randomness needed in Proof-of-Work?

In Proof-of-Work (PoW) mining, a miner that contributes 10% of the network hash rate will on average receive 10% of the mining rewards. “On average” means that 10% of blocks are mined by this miner, and 90% of blocks are mined by other miners.

In practice, basically all miners join mining pools which removes this randomness, i.e., pools pay miners deterministically based on the hash rate they supply.

My question is: Why is randomness needed in the PoW protocol? Specifically, if a miner supplies 10% of the network hash rate, why cannot this miner simply receive 10% of the mining reward for each block?