Often the companies combine IT operations, or purchase fuel and aircraft as a bloc to achieve higher bargaining power. However, the alliances have been most successful at purchasing invisible supplies and services, such as fuel. Airlines usually prefer to purchase items visible to their passengers to differentiate themselves from local competitors. If an airline's main domestic competitor flies Boeing airliners, then the airline may prefer to use Airbus aircraft regardless of what the rest of the alliance chooses.
I would recommend Naxos over Mykonos and with 12 days you could easily add Paros too. With Santorini, Paros, and Naxos you’ll get a good mix of different delights and some ferry island hopping too which is fun in itself. 1.5 days in Athens is perfect for most – 1 day for the Plaka, Parthenon, Acropolis Museum area; and a half-day to visit the Archaeological Museum which is a short drive or walk from the Plaka but hard to fit in one day along with the other sights.
Crete, Santorini, and Naxos look quite doable within the 12-day block, but Crete’s beaches are scattered throughout a very LARGE island, Santorini really only has Kamari and Perissá (and some southern coast bays) and Naxos does have nice places to swim. If you choose only to visit those three islands in your relatively short time, you will do well.
Airlines have substantial fixed and operating costs to establish and maintain air services: labor, fuel, airplanes, engines, spares and parts, IT services and networks, airport equipment, airport handling services, booking commissions, advertising, catering, training, aviation insurance and other costs. Thus all but a small percentage of the income from ticket sales is paid out to a wide variety of external providers or internal cost centers.