I am aware of the demand, I just don’t understand the reasoning behind it. I think the whole idea is something people copy by example, without a solid reason.
Arguably, if MC(MC) results are significantly affected by the initial state of the RNG, they are anything but reproducible, and could be considered spurious instead.
The only valid use case is probably debugging in some contexts, as described by @tkf above. This is a nice property, but I am not sure it is worth insisting that the default/generic RNG satisfies this, especially if it involves other trade-offs.