I would however not stop with that, but also incorporate a hydro-electric scheme whereby turbines generate power as the water being transferred passes along the 'trunk' route pipes. This would resolve two pressing issues at once
Not wishing to pour cold water on that (see what I did there? ), but I thought hydro-electicity is only powered by gravity (e.g. waterfalls or rivers). If the water is pumped across a grid, then the energy used to pump it would be absorbed by the hydro plants, thus nullifying any benefit.
Indeed it is, but with a new water trunk system, designed for the purpose across terrain of many gradients, there would be certain parts that would 'fall' and there is the place for giant turbines.
Of course natural physical law dictates you cannot get more energy out than you put in, and the pumps along the system, as with the local pipework, would require electrical power (much via solar panels/wind turbines?), which is unavoidable, but at strategically located sites, where the gradient falls, highly efficient turbines could be placed to generated significant power, some of which could also power the pumps.
To advance society must continue to think outside the box, as did the great engineers of the 18th and 19th centuries did when building the canal and railway network.
Of course all this blue sky thinking means spending money....big money..........and is one reason why no government has yet considered a National Water Grid of the style that the leccy boys use. I reckon 500 billion pounds will do it.............well, as that figure has been guessed, via a wet finger in the air........once the project is started it will cost 800 billion pounds...................rising to £1 trillion once built six years after it's planned completion date!!
Seriously though, the basic Water Grid idea is a sound one and will be ever more important as the climate DOES get hotter, no matter for what reason, our population grows considerably and people 's demand for the stuff for swimming pools, jacuzzi spa baths and growing our crops rises still further