Where I think you're correct is that typical AI data centers require a LOT of cooling, and to achieve this at scale would require enormous radiators. So large that it's hard to square the business case given current launch costs. I've read a lot of research in this space and it looks like the much more realistic use cases (at least at first) will be sub-processing. Meaning processing data already in space. These could be telemetry, Starlink, tracking, telescopes, logistics, military, GPS, weather, deep space missions, first-response, alerts, etc. In particular, applications which require lower latency.
There are also other applications which are less cost sensitive. For example, applications which might be banned on Earth, or at risk of espionage, attack, or intrusion.
If we want to make typical AI data centers in space to be economical, we need launch costs to drop to under $200/kg. Interestingly, [Starship could reduce costs down to $67/kg.] Even lower with >9 launch cycles. (https://arstechnica.com/space/2026/07/rocket-developers-used...) This would make the business case *extremely* attractive.