So a system to recirculate the same 24 gallons per minute would be more expensive than $100k per year for water?

Condensing the steam back into water would undo the cooling power, so yes. Massively less efficient. Negative efficiency, as required by thermodynamics.

Your only gains would come from whatever increased surface area the system has, radiating energy however it can. But a radiator without any water involved would be as good or better. Air-cooled datacenters do exist, they're just trading other costs and usually can't release as much heat.

Evaporating a gram of water is 2260 joules. Evaporating 20 gallons per minute, 1/3 of a gallon per second, gets rid of around 3 megawatts of heat.

If you had to use heat pumps to move all that out of the water, you'd have to spend about a million dollars on their electricity. If you're somewhere that you can use unassisted radiators all year, great. If you need to force the heat out part of the year, that easily gets worse than boiling off water.

Apparently so