The supply side of power generation is coordinated by a bid system. So the cheapest sources are activated first. As demand goes up increasingly expensive forms of power generation are turned on.

For daily and seasonal variation, this is fine. The amount of time that really expensive generation is active is only a small portion and the base rate can stay low. However, if you add a bunch of baseload without adding equivalent generation, your utility will be stuck buying at the top end of the capacity market auction. The datacenter will have negotiated a discounted rate though because constant demand is good for the utility in the long run. That leaves everyone else paying a big rate increase.

Source: none given, but the capacity auction is a real thing, and the predicted behaviour of such a system can be reasoned.