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Some facilities is do this. They're not 100% efficient, so some is lost to evaporation, some must be dumped because it has too much mineral content (and too much conductivity) to go back through the cooling system. Reusing is only about 50% efficient (according to Google's numbers).

On a standard PC, you can easily have a loop because the radiator is big enough to exhause all that heat. But when your computer or cluster puts out multiple thousands of watts of heat, eventually you need to get rid of tge hot water and replace it with cold water. And when it gets even hotter, you need a steady stream of cold water that immediately gets dumped.

Half a liter per kilowatt hour. That's the average water use

It's like the idea of recycling plastics with water.
Not all of it is reusable to the same degree. A good portion of water has to be evaporated off to cool down the exterior towers plus water isn't really infinitely usable in these loops. It gets gross or full of materials.

Another thing that people need to remember is generating electricity uses the water here as we literally don't use many methods that don't involve water, we are not on a green grid and neither are these huge data centers for the most part. We boil it for the electricity then have to use additional to clean the system after.

If you live in a low humidity area you can cool with an evaporative cooler cheaper than with air con. Evaporative coolers consume quite a bit of water

Not really. Look at California agriculture. You've got immense and unsustainable amounts of water going to almonds, pistachios, and other cash crops (not to mention animal feed for the Saudis) with voracious demand for more water, despite it causing damage to the water sources.

If you can't imagine a world without eating meat, yes.