I've made both pita bread and naan recently and both times the result have had tough crusts. They each have puffed exactly as they should have but the results have been too chewy. Each was made with King Arthur regular flour which is fairly high protein and the dough was kneaded in my mini Bosch for 6 mins. The pita were rolled thin, cooked on a hot cast iron skillet, puffed to a complete globe and 'looked' perfect. The naan used the same flour with full fat yoghurt, yeast, a pinch of baking powder water and salt. I cooked them in a hot cast iron skillet after wetting the underside slightly and covering the skillet briefly, then putting them under a very hot broiler to finish the top - the idea was to imitate cooking with a tava. The naan looked good, had lovely bubbles and were tough.
I'm a fairly experienced baker with both yeast and sourdough loaves which generally turn out fine. I thoght flatbreads were supposed to be 'easy'.