Or is it building the infrastructure to accommodate them the issue?

It’s this, but that’s only part of the story.

Datacenter companies are very efficient at building new ones now, once they have all the proper permits and can start building it can go from an empty lot to fully functional in a year or two. Maybe longer for the huge hyperscalar ones.

Once they are online, their power demand is comparable to a small city, coming online all at once. But the local utility never had this demand in its plan, so they have to build more capacity to service it, and building a new power plant takes much longer. In the meantime, the demand will outstrip their capacity and the utility will have to buy more power on the open market. This drives up costs for all their customers unless the utility is allowed to charge these customers (whose existence has blown up all their capacity planning) more.

As a side note, they often get advantages and tax breaks because they promise to bring jobs to the area. And the initial construction jobs usually are significant. But once the place is built, it’s ongoing operations only requires a few dozen positions, many of them low-tech and outsourced like site security. The higher-tech jobs (like the network engineering) is often not on-site anyway. A shopping plaza would generate more jobs than a datacenter.