As for the speed, SHA512 is faster to compute compared to SHA256 in modern hardware so there is no benefits there either.
Isn't speed a benefit? And not only speed, but computational expense.
It depends on the context. In context of brute forcing, it is not a benefit. Mining is a form of brute forcing too, so in a way you don't want to introduce an algorithm that can be computed faster than the existing one. You usually want to make it harder when replacing an algorithm.