Most immediate advantage is latency for space-based Internet relay. I can see a market for low latency /real time applications. I think the issue here is that we have to re-think what "the edge" means here, since locality of data is literally changing by the second. Maybe a by-space-for-space data service? An interesting question is data sovereignty. Whose jurisdiction does it fall under? Relay-focused satellites sort of skirt around the issue, but a orbital data center is going to be different.

Isn't a major issue how to disperse heat in space? That seems bad for data centers.

From the man who promised us self driving cars in the last decade.

No, it won't.