The problem is when water evaporates and come as a rain, it is distributed. And, we need large amount of fresh water in one area. Additionally, you are not considering the time closed loop system takes to replenish the water source.
I agree with your last point. However, I think they still can filter and make it harmless, but we know there is no incentive to do that and the cost is high.
In a large river basin, there is a very high chance the water falls again as rain into the very same river it was extracted from. In that case, it's a closed loop system.
This is unlike other water uses, like washing wafers, where the water will end up in a sewer and eventually into the sea.