It's been calculated that these (plastic) devices could easily be manufactured in the poorer nations where the cost of living is low, and therefore where fair salaries are also low. This would boost those nations' economies while producing a device that could be sold at a profit for five dollars. A practical-size solar still will produce one liter of clean fresh water per day in a sunny, warm climate--which happens to be where most of the people live who desperately need clean fresh water. One liter isn't a lot but if used wisely it will make the difference between dysentery (still the leading cause of child mortality in many countries) and health for hundreds of millions of adults and children.
A wealthy philanthropist like Bill Gates or Warren Buffett could provide one of these to every person on earth who needs one within ten years (politics and logistics would surely make it impossible to distribute them any faster than that anyway, considering the kinds of governments most of those countries have), without using up his entire annual charity budget.
They can use just about any kind of water as input, including polluted rivers, industrial effluent, or even plain old sewage.
Another worry about fresh water is the depletion of glaciers that feed all the major rivers. Presumably there will always be snow melt, but imagine that becoming the new normal. Then if a dry spell were to set in, you could imagine the Nile or Yangtze going dry. It would be a disaster.
But don't forget that as the average temperature rises, so will the relative humidity. Ice ages always bring drought and warm spells always bring rain. This will feed the rivers as well as delivering rainwater directly to many places that now have to pipe it in. The Sahara may once again be a breadbasket.
It was an epochal drought and famine in Africa during the depths of an ice age 60KYA that encouraged a band of the San people (or "Bushmen") in desperation to walk out of Africa into Asia in search of better weather. They got all the way to Australia before they found what, to them, (due to the vagaries of weather patterns) was paradise. Remember that during an ice age more of the earth's water is locked in permanent icecaps and glaciers, so sea level is lower. The distance between all those islands was narrower, making the voyage practical in Stone Age-technology boats.
The San people still exist (although they now live much farther south due to the desertification of North Africa as the ice age ends--the increase in rainfall is not uniform across the entire planet) and DNA analysis proves that they are, indeed, the ancestors of all non-African people. (I've oversimplified the story, there was a second San emigration 10K years later which populated the other continents.)
I like this idea of deriving fresh water from sea water. I think it's forward thinking. It would be interesting to live on an island where everybody was on the same page with ideas like this and cooperated to really do something completely new and different that actually worked as as far as low-impact living is concerned.
Average rainfall will increase on islands just as it will on the continents. The biggest problem islanders will face as this ice age comes to its ultimate termination is the rise in sea level. Most of the smaller islands like Manhattan and the Maldives will simply be under 50m or more of water, as will Florida, Bangladesh, Holland, and a majority of the world's cities.