> But population doesn't (in my opinion) determine importance. For example, the capital is a very important city even if not the most populous.
It goes the other way. Importance determines population. If the capital is not populous, that reflects the fact that the capital isn't especially important.
But assuming you're in a more or less steady state, that effect has already happened, so it's perfectly valid to just assume that importance and population are tightly correlated. The directionality doesn't really matter to the result.
Does it though? You still have provided no supporting arguments for that. People live in places for reasons beyond importance. In fact, "importance" really isn't a factor people consider when they decide to live somewhere at all really in my experience.
It goes the other way. Importance determines population. If the capital is not populous, that reflects the fact that the capital isn't especially important.
But assuming you're in a more or less steady state, that effect has already happened, so it's perfectly valid to just assume that importance and population are tightly correlated. The directionality doesn't really matter to the result.