Correction: Cape Town is *not* any known definition of a "Western" city.
The West geographically refers to Western Europe and North America, and Cape Town is part of neither.
Culturally those areas dominated by the culture that came out of  Anglican Western Europe can be added - so once could legitimately refer to Australian and New Zeeland as part of the west. But this isn't true of Cape Town either - the largest 3 cultures in the city are ALL African native cultures (although two of them Afrikaner and Coloured culture have some strong Germanic [not Anglican] influence - both are still African native cultures).

So, if Cape Town does run out of water, there still wouldn't be a single example of a Western city ever having done so. Not least because all the ACTUAL Western Cities are built on continents that get more rain than they can ever use up and where droughts are extremely rare once-in-a-millenium events. They worry more about floods and hurricanes, not droughts.