People can always move. Where the people live isn't particularly relevant, though. In the way other states can become cultural or economic centers, a state could easily become a political powerhouse if it hosted the country's capital. That's why so many places use districts for capital cities, instead of states/provinces/territories/whatever.

Consider it a check on potential power, if you will. We have checks on the branches of government so they don't become too powerful and become the government. We have civilian control of the military so the military doesn't become the government. And we place our capital city in a district so no one state has additional leverage politically by virtue of hosting the capital...becoming the capital, instead of a state.