The way I understand is that they would use a sun-synchronous orbit, more specifically a dawn/dusk orbit, which places the satellite over the terminator between day and night meaning it always directly sees the sun. But yes, it would need an insane number of solar panels. What's more, data centers don't just need power, they also need cooling. So there would also need to be an insane amount of radiators (in space it's very hard to get rid of heat).

All in all the only advantage I can see is not much of an advantage, if at all, especially compared to all the drawbacks.