Tx nonce question

Please correct any of the following. Ethereum, as I understand it, uses a transaction nonce to avoid replay attacks. It's an index which increments each time ether moves out of an address, right? Why did Ethereum choose to enforce such strict ordering of the transaction nonces? Wouldn't it be enough to disallow the same transaction nonce twice? Is the issue that it takes too much time to search the entire blockchain looking for the duplicate tx nonce?

Submitted December 21, 2018 at 08:38AM }
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