One of the prototypical payoffs that could be had with self-replication that I have seen mentioned is solar farms in the desert that live off sand or rocks and produce arbitrarily large acreage of photovoltaics that can then be used as a replacement for oil. This requires full self-replication, including chemical raw material processing, which is not easy to demonstrate.

I am not sure a good business case could be made for the more limited form of self-replication where the "raw material" is machine parts that only need to be assembled. That would be much easier to demonstrate, so I think a business case for it would be extremely valuable.