The big cities will thrive on their own, sure, but their tax money would then no longer be used to help people in the more remote regions.

As an Australian, I assure you it is possible for a country of "big cities" to fund activity in remote areas. I won't say we do it a perfect job of it here, but we do a decent enuogh job and some of our remote towns are far more remote than anything in the northern hemisphere. Some Australian towns are several hours by airplane to the nearest city and don't even have a reliable source of water. And yet, the people living there have relatively comfortable lives.