"Suppose Bitcoin mining software always explored nonces starting with x = 0, then x = 1, x = 2,\ldots. If this is done by all (or even just a substantial fraction) of Bitcoin miners then it creates a vulnerability."
The reward for mining the block includes the miner's account, so each miner is hashing a unique block.
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In answer to the question:
"Suppose Bitcoin mining software always explored nonces starting with x = 0, then x = 1, x = 2,\ldots. If this is done by all (or even just a substantial fraction) of Bitcoin miners then it creates a vulnerability."
The reward for mining the block includes the miner's account, so each miner is hashing a unique block.