The water has to be expelled somewhere, and as your rubber exhaust hose and rubber or plastic exhaust silencer would not be able to withstand the heat of the exhaust gasses, the water is injected into the exhaust via the exhaust injection bend immediately aft of your manifold heat exchanger. The water now in the exhaust line between the engine and the exhaust outlet now cools the exhaust temperature to below that where its temperature might otherwise harm your exhaust hose and silencer, but it then also shares the same overboard outlet, thereby reducing the number of overboard outlets by one.
So in short the water temperature is used for cooling wherever it can, you have saved the cost of higher quality materials that might otherwise be capable of taking the exhaust temperature on their own, you have removed the need for insulation around a solely exhaust gas line to overboard, the introduction of water into the exhaust system has reduced the exhaust noise in addition to its cooling benefit, and you have saved the cost of an additional overboard skin fitting. ...... Sounds like a bargain to me