> power seems like a weird metric to use

Because this technology changes so fast, that's the only metric that you can control over several data centers. It is also directly connected to the general capacity of data center, which is limited by available energy to operate.

To expand on rahimnathwani's comment below - the big capital costs of a data center are land, the building itself, the power distribution and the cooling.

You can get a lot of land for a million bucks, and it doesn't cost all that much to build what's basically a big 2-story warehouse, so the primary capital costs are power and cooling. (in fact, in some older estimates, the capital to build that power+cooling cost more per year than the electricity itself)

My understanding is that although power and cooling infrastructure are long-lived compared to computers, they still depreciate faster than the building, so they dominate costs even more than the raw price would indicate.

The state of the art in power and cooling is basically defined by the cost to feed X MW of computing, where that cost includes both capital and operation, and of course lower is better. That means that at a particular SOTA, and at an appropriate scale for that technology, the cost of the facility is a constant overhead on top of the cost of the equipment it houses. To a rough approximation, of course.

And cooling capacity.