Using electricity is not breaking anything. "If I sell all my widgets, it's actually a good thing because I'll have to hire more people and manufacture more widgets" is entirely coherent.

Using electricity to the point that the grid cannot accommodate it is indeed breaking something that was working before, and the data center folks are surely not going to be the only ones paying for the infrastructure improvements needed to accommodate it.

It'd be like your widget maker harvesting wood for their widgets from public land and exhausting it so the public is left without this resource, then expecting the public to pay to arrange for more wood to be grown to replace the wood they used up.