People who can't pay a lot of money for an airline ticket still might have important things that they want to take on the trip. They shouldn't be disallowed from having a carry-on bag, because they should have a right to have valuables stay close to them, too. There should be a better way.
If American Airlines is going to ban carry on bags, then they should ban them for everyone and not just economy passengers. A better idea would be to limit the number and size of carry ons , thus affording everyone the same options. Why single out the economically challenged people, like is done in so many other aspects of life?
What is American Airlines going to do next, ask economy passengers to only enter the plane with the clothes on their back? People fly because the distance is too great and if you're going somewhere so far away, you need to take personal items with you. It's not like the aircraft doesn't have the capacity to hold a single carry-on bag for each passenger.
Banning carry on bags for economy passengers on American Airlines is not a good PR move. This will likely cause a lot of outrage as a majority of passengers fly economy. Flyers will look for other airlines that allow carry on bags. There is no good reason for American Airlines to ban carry on bags.