After the 1960 census Milwaukee was one of the ten or twelve largest cities in the U.S. It's no wonder they were considered a top National League city at the time. The Midwest was really a "frontier" major league baseball back then. When the Dodgers and Giants moved to the West Coast in 1958 they were the only big-league baseball teams west of St. Louis. That's pretty remarkable, when you think about it.
Your points about Cincinnati and Pittsburgh are valid (and St. Louis to a lesser extent, though that is not exactly a "small market" by any measure), but keep in mind that those cities have had long traditions of big-league sports that go back many decades. Cincinnati was one of the original National League franchises, Pittsburgh was one of the top ten cities in the U.S. until around 1950, and St. Louis was such a prime baseball that it once had two big-league teams (the Cardinals and Browns).
And, BTW, your knowledge of geography and baseball history could stand a little improvement. When the Dodgers and Giants moved to the West Coast, Kansas City, not St. Louis, was the farthest west city in the major leagues. And no, Milwaukee was hardly a "frontier" in the 1950s, since it is only 90 miles or so from Chicago, which had had major league baseball since the beginning of the sport..
After the 1960 census Milwaukee was one of the ten or twelve largest cities in the U.S.
Just looked it up. It was 15th in population in 1960 with a population of roughly 735,000. Among NL cities, it ranked 5th of eight in population, trailing Chicago, Los Angeles, Philadelphia, and St. Louis, and exceeding San Francisco, Pittsburgh, and Cincinnati. I don't have the metro area figures on hand.