Well many Capital are among the 50 largest cities. Phoenix is number 5. Austin, Sacromento, Denver, Oklahoma City, Boston, Atlanta, Nashville, Columbus, Indianapolis, are among the top 50 largest cities.
State capitols were established as
A) Central Locations (Pierre, Bismark, Springfield, Madison, Montgomery, Jackson etc…)
B) Compromises between two larger cities (Jacksonville and Pensacola were the large cities in Florida. The only other city of real importance was Key West. Most of FL south of those cities was conidered a swamp. So halfway was BOOM Tallahassee. Jefferson City between KC and Saint Louis. Frankfort between Lexington and Louisville)
C) To balance one city states (I know I’ll get lot of arguments here but…) Chicago dominated Illinois. If you put the capitol there what else would there be…
NYC dominates NY State. Although there are many big cities the enromous population of NYC. Almost as big as the next three larges cities in America would be too dominant.
The counter argument is small states both physically (Boston and Providence…The state is so small why bother moving it) and population wise Utah…Idaho that it made no sense as central areas of those states were not really habitable. (at the time)
Then of course the Western and Southern state have experienced population booms. Phoenix didn’t have 100,000 in 1940 today it has 1.3 million. Austin and Sacromento are other good example of massive population booms.
State capitals don’t suffer the population declines that traditionally large cities do. For example Pittsburg isn’t even in the top 50 cities any more. Cleveland and Saint Louis have bled people. Cinicinnati will likely fall behind Toldeo by next census.
I can only think of a few capitals that have lost a bit. Salt Lake City, Providence, Atlanta but they have lost their people to their suburbs and the drain hasn’t been massive.