The Mediterranean isn't quite the bonanza you think it is. Look around the Mediterranean itself, and its history, you have a bare scratchy existence, the most violent area in history as the differing nations massacred each other for millenia over the scarce fertile areas around rivers and their valleys.
Look at the Geography, how much dry sandy soil there is, as topsoil cant stay during the dry season. Besides Italy and Turkey, you have all historically poor nations. And Italy's wealth is all concentrated in the North, which is temperate, and built around the Po river valley and its tributaries, watered by Alpine snowmelt.
The Mediterranean is of course, the most comfortable climate, a paradise to visit, I love it, Im from Greece. My country of origin has ALWAYS been poor, the inhabitants scratching out a bare living from dry rocky soil. Even in its golden age. During those years of artistic and cultural magnificence, Greeks were spitting out much of the population to build colonies as far as Marseilles, France, most of Sicily and South Italy, the black sea coast of Ukraine. Because the land was incapable of feeding the inhabitants, Greeks imported a large percentage of its staple wheat, paid for by exports of olive oil, wine, and silver from Athens Laurium mines.
There is a reason the Temperate zone of Europe - France, England, Germany, Russia created the Global superpowers that conquered the Americas in 1500-1600's, and the rest of the world in the 1800's. Mediteranean Spain's dominance was very short, eclipsed by 1700, Temperate is WAY more productive, the rainfall keeping the rich black soils in place. Why do you think USA became a superpower and its main rival was Russia? Possession of vast amounts of fertile land, in a temperate zone as well as blessed with almost every resource an Industrial Economy could use.
Mediteranean climate is DRY. Little or no rainfall. The coast is beautiful, but barren. Maybe what your dreaming of is the subtropical climate of the American south, which is very productive.
And what are you thinking when you say the population should "Move to these zones"? Do you imagine the area to be as empty as the vast square states of the USA? You can tell what areas can be settled and can produce food by the amount of green vegetation growing wild. In the temperate zone of Europe and America, the sides of the road, and vacant lots in the cities are covered and overgrown with wild grasses (what a lawn owner calls weeds) and trees sprout out of nothing. Even the cracks in the sidewalk sprout green. Pay attention to population concentration historically; The breadbaskets of the Earth are the centers of the highest populations. Why do 2.3 billion people live in China and India and not the Mediteranean? Subtropical rice production, high rainfall and hence, many river valleys.