There are countries where they do, with notable examples being Kuwait, Puerto Rico, Djibouti, Mongolia and Uruguay.

Since rural populations are declining everywhere, relative weights of urban populations, as well as those in the largest cities, are increasing, so largest cities now are more dominating than they were in the ’60s.

The most concentrated region seems to be East Asia, but that is because they have Hong Kong and Macao with almost 100% of people living in the only city.

What: Median proportion of the population in the largest city, the urban area without the largest city, and the rural population.
When: 1960 and 2019
Where: The whole world, with some exceptions having a total of 26 million inhabitants, the biggest being Botswana, Lesotho and Slovenia. Many of those exceptions are small, possibly one-city countries which do not have needed statistics in the Worldbank database.
Source: Worldbank