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.