Air cooling is feasible, as evidenced by existing power stations that use air cooling. A lot of newer nuclear generation use water cooling, being sited along the ocean and in the multi gigawatt range. But we can also find examples of inland power stations that have no water connection, and therefore need some massive cooling towers. Here is one in Germany that has a 2.2 GW rating and a 200 meter tall tower: en.wikipedia.org/wiki/Niederaussem_Power_Station

This is, as you can imagine, rather expensive to build, but it’s doable. Cooling a coal fire is not substantially different than cooling compute loads in a data center, as it’s all just a matter of moving heat around. Will there be differences due to the base temperature of coal versus GPUs? Yes, since the ratio of input to ambient temperature matters. But on the flip side, this should make it easier to construct, as the plumbing for lower temperatures is simpler.

Mechanical engineers can chime in on feasibility for AI data centers, but seeing as it hasn’t been done, its probably still cost related.