The main point of leasing versus buying is to conserve cash up front and offloading the liability to the lessor. You're still paying the lease payments but it gives you the ability to do something more beneficial with the cash you didn't have to pay upfront. Leases can also be renegotiated in bankruptcy.
If you previously owned or were making payments, it is also possible to transfer ownership to an aircraft lessor. You receive cash up front to purchase the aircraft then make regular lease payments.
I think you totally misunderstood how AA got their aircraft. They bought many aircrafts with financing, i.e. debt. They did not pay cash up front for the aircraft. It is no difference with lease, except AA pays interests and incremental repayment for the finance. Other airlines that is heavy on lease pay a monthly lease based on usage, with the option to buy out after 10 to 12 years.
Think this way, airlines like Norwegian lease their aircraft is like leasing a $50,000 car from dealer on a 2 years contacts, paying $500 per month plus excess mileage. Airlines like AA buys the car with a 3% financing deal, only paying a monthly payment and interests. If AA is to keep the car for 10 years, the monthly payment is less than $430. Less than the leasing price. [numbers above is fiction and only serves the illustration purpose].
Depends on the deal, buying aircrafts with long term financing option is good for airlines with long term vision. Leasing aircrafts is good for the first few years but ultimately could break an airline (look at Norwegian). If Leasing is so good, you would see all airlines funding all their aircrafts through this way. But the reality is there are plenty airlines have a smaller number on lease yet keep a lot through financing.
Sure, AA has a problem with high debt now with aircraft financing, but as long as financing company and aircraft manufactures see nothing wrong, or AA has enough cash reserve or ability to access cash, things will become good eventually, and AA could be ahead even after the magical debt maturing date. But look at Thai Airways with their restructuring, what is happening to their leased aircraft, and other airlines that caught between on-going lease payment even the aircraft is not flying...The truth is, there is no certain way to judge which way is good until it happened. At this moment we can only speculate and make comments.