Hello, Shana. I imagine we're talking about two or more cities. If we use the structure with "of", then it's "(the) populations of (the) cities". However, there is another option where we use the singular even if there are multiple cities: "(The) city populations" (I guess this is "Chinese style"). Note that in this case, the article refers to the populations, not the city. In fact, we usually use a singular noun in such constructions — for example, an "egg carton" may contain 12 eggs (or whatever), yet we do not say an "eggs carton". An option with a slightly different shade of meaning would be "The cities' populations". Note that in this case, the article refers to the cities, not the populations. Note that it is also possible for multiple cities to share "one population" (i.e. a number representing the sum of the individual cities' populations). Note that "cities" and "cities" or may not be preceded by the definite article (depending on the meaning).

Interestingly, you need the plural for city in the construction ‘of cities’ but you don’t always need it for ‘population’! The population of cities might decline if remote work continues to gain in importance. (Collectively, one population) The populations of cities in Texas are growing. (More than one city, each with its own population)

Yes, it's necessary. You are talking about more than one city!

Yes, with more than one city you'd need to say; cities. Nick, Professional English Teacher

If you are talking about more than one city, then it's okay to say 'population of the cities' but if you are referring to one city, you can simply say,' The population of the city.'