"Recirculating" water isn't thermodynamically the same. Evaporating the water is THE POINT of the system. You can make closed-loop coolers but they use more energy.
Which makes the often repeated excuse "Closed loop datacenters exist" to refute water use concerns a bit nonsensical.
It's all contextual. If the energy inputs are carbon-free and local water is scarce, then for that given situation a closed-loop system might make sense. People are building such a thing in Tucson, Arizona right now.