> the cooling water from rivers cant be used any more to cool the reactors. So much about being future proof.
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.
Not all need a river to cool but every single nuclear power plant needs a consistent water source 1) to actually generate the energy (steam!), 2) to cool, 3) as emergency safeguard when things go wrong. If you followed the news about Russia's attack on Ukraine and the risks to Zaporizia much of it was about fear of an incident, among others due to water sources or the energy to bring water to the plant being at risk
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.
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.