Most of zones have mid level FATEs. Some of them even have enough FATEs that don't require 50s to sync that a level 50 can grind exclusively on them.

Central Shroud has Sorrel Haven and Spriggan Dig.
North Shroud has the areas surrounding Fallgourd Float.
East Shroud has Sylphlands.
Western La Noscea has the area west of Camp Skull Valley.
Upper and Outer La Noscea are not low level zones.
Eastern Thanalan has everything east of Drybone (Burning Wall).
Southern Thanalan has Zahar'ak and Sagolii Desert.

That leaves Middle La Noscea, Lower La Noscea, Central Thanalan, Western Thanalan that are exclusively low level zones. That's 25%. Not a majority at all.