Also, even it were provably true that some hash algorithm has this property, we would have to implement it properly. That requires the algorithm itself as well as all of its dependencies to be implemented properly. It's very easy to make an implementation mistake that breaks security.
Is that typically a problem for a plain hash? There's no random data to be leaked or generated poorly, and there's typically not going to be any private information that could be leaked through a timing attack.
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Also, even it were provably true that some hash algorithm has this property, we would have to implement it properly. That requires the algorithm itself as well as all of its dependencies to be implemented properly. It's very easy to make an implementation mistake that breaks security.
Is that typically a problem for a plain hash? There's no random data to be leaked or generated poorly, and there's typically not going to be any private information that could be leaked through a timing attack.