There are more reactor types than water-cooled reactors, and modern energy plants should use cooling towers even if some water reservoir is available, nuclear or not.
> it is because they are completely uneconomically
This is why private sector cannot provide infrastructure. State is not a company.
> Hint: it is because they are completely uneconomically
Yes, natural gas and fossil fuels were cheaper than nuclear too. That and the irrational panic is what killed it. At this point its probably too late (and renewables are more feasible option unless there are some significant technological advancements), but if you add up all the long-term costs and externalities nuclear would have turned out to be much cheaper in the 80s and 90s than it seemed on paper.
Just coal alone used to kill (probably still does worldwide) more people every year than Chernobyl ever did... What is the cost of that?
Secondary loop can be made closed system. This reduces efficiency, but this could be acceptable considering water scarcity. Of course there would be some leaks etc. so water needs to be resupplied, but in much lesser amounts.
> 2) to cool
Not necessarily true, because primary loop doesn't need to have water (HTG, MSR, LMR reactors). HTG reactor actually doesn't need water at all and can power gas turbine directly. LMR, depending on chosen coolant, can do this as well, though it requires heat exchanger.