Yes, Euria and many others in Europa are already doing it.

https://euria.infomaniak.com/

The Problem is not AI but how Datacenters are used in USA.

And closed-loop cooling. But then it will still emit heat, which should be captured in a downstream process.

We need that for more important stuff, especially because the effort to replace fossil fuels with renewables is lagging. You don't get to just add new huge energy uses while the old ones haven't been moved to renewables.

As long as fossil fuel energy is put on the grid, there is no such thing as running on renewables alone.
For every Watt of green energy you use, someone else uses one less and that gap gets filles by fossil fuels.