
Minimum wage has nothing to do with that. The reason why it is expensive is because of the demand and the overcrowding of people there. Because there are so many people living in those cities, those landlords raise the rent prices to basically create competition. So if you have 200 people applying for only 20 open apartment. Landlords are going to raise the rent to see who is willing to pay those prices, regardless of the minimum wage.
Because it's cheap! That's the point. Businesses are moving there because people are, and there are more people to hire because of it. If the minimum person in Alabama can suddenly spend another 5K a year, then prices will immediately rise to match that. It will just worsen the inflation we already see.