Sure, things would be different if the cost was $1/kg, but short of somebody building a space elevator that's just not going to happen.
But are you sure that $100/kg is not competitive? I don't remember all the math, but even their initial AI1 design[1] would throw a lot of profit, if you can sell at the price they offered to Anthropic.
I suspect the price of manufacturing the satellite, plus chips, is the dominating factor, not necessarily the launch costs.
If you want math then https://andrewmccalip.com/space-datacenters exists. The numbers are grim for orbital DC. Even if you drag the launch cost slider all the way to $1/kg (by the way this is literally sci-fi, per ChatGPT air freight of semiconductors from Taiwan to Ohio costs $9/kg and ocean/train freight costs a bit under $1/kg for a reasonable shipment so good luck with $1/kg to LEO this century) it is still more than twice as expensive as terrestrial DCs.
A 1GW datacenter with chips operating at 100C (which is probably doable) will need a radiator that has a surface of one square _kilometer_, and this is with all the favorable assumptions. Realistically you'll need about 2x of that.
If you want your DCs to be on a 1000km orbit (for reasonable ping times), you'll be able to _resolve_ these satellites with a naked eye!
Sorry. But this idea is fundamentally unworkable.
Deploy 4,000 and you're at 1 GW. That's 160 launches.
BTW: SpaceX has already manufactured and launched 10,000 Starlink satellites and Falcon 9 launches about 150 times per year. None of this seems unworkable.
Look at the numbers. 1kW of nuclear power capacity on Earth is around $2000, and that's 24/7 guaranteed power. So a 250kW cluster needs $500000 to cover its power demand with near 100% reliability and with some ongoing cost.
And if we're OK with some interruptions, then we can use solar+wind at around $100000 and with essentially no ongoing cost. If we assume the absolutely best projected launch cost of $100 per kg (vs the current one of ~$800), that's just 1 ton of material in space!
So you're off by 2-3 orders of magnitude in cost. And this kind of "it's unprofitable" is actually a fundamental issue.