I've heard arguments that cooling will be a hard technical challenge and, given current equipment weights and launch costs, they would be uneconomical. But is there an obvious reason space data centers would be impossible?

Most technologies start out looking hard and economically infeasible. But if you invest in development, you might be able to get a few breakthroughs, and suddenly, it's viable.

If they do get things to work, the benefits seem obvious: 24/7 access to clean energy, not upsetting the people who'd rather not have a datacenter next door (or in the same state), and plenty of space to scale up.