Yeah, I think surrogate gradients are usually used to train spiking neural nets where the binary nature is considered an end in itself, for reasons of biological plausibility or something. Not for any performance benefits. It's not an area I really know that much about though.
There's performance benefits when they're implemented in hardware. The brain is a mixed-signal system whose massively-parallel, tiny, analog components keep it ultra-fast at ultra-low energy.
Analog NN's, including spiking ones, share some of those properties. Several chips, like TrueNorth, are designed to take advantage of that on biological side. Others, like Mythic AI's, are accelerating normal types of ML systems.