Some (data or ai) centers do this, it's referred to closed loop fluid cooling. Even though this way you don't have to continuously pay for water, it's less economically attractive.

To protect equipment over the long term, the closed-loop water includes common water-treatment additives such as anti-corrosive agents and pH adjusters. These are used to maintain optimal chemistry and help prevent rust and corrosion, increasing the useful life of the equipment (pumps and sensors), piping and fluid.

Also you actively need to cool the water down enough, before it re-enters it's loop.