And the sad part is that ai would be a perfect fit for intermittent energy sources: run inference 24/7 (on whatever you can muster, even if it's fossil it simply does not consume all that much compared to training) and over-build training to achieve whatever total throughout you need in time of energy abundance. How heavy would CO2 pricing have to be to make the market do this instead of the exact opposite?

You can't price out these people, they have seemingly unlimited money.

What would be the economy of these data centers if they would run using power source with say, for example 25% capacity factor? What is the capital expenditure of a data center? What is the yearly operational expenditure of a data center?

I found that a 100 MW datacenter can cost roughly $3.35 billion, with a significant portion going to high-end GPUs like the B100 or H100. For electricity, 100 MW data center can incur annual power costs ranging from $41 million to over $131 million, depending on regional energy prices.

Compute has massive initial capital requirements, and a very short obsolescence window. It does not make sense to invest in compute and then not run it 24/7 at 100%.

Hardware sitting idle waiting for sunshine/wind is leaving money on the table. Especially if you can burn gas during that time and still be hugely profitable.