Xeque: Let me get this straight. You are saying that the only reason for carrying economy class passengers is to pay for the platform that supports First and Business?
As TheOddOne says, that's absolutely right.
Current philosophy is that if you fill the Y cabin, you'll pay the overhead costs of operating the aircraft. The premium cabins then provide the profit.
Of course, there's a symbiosis. If you can fill lots of Y cabins, you can offer a higher frequency. If you can offer a higher frequency, your premium cabins will become more attractive to the pax who pay for them, who are largely pax for whom flexibility is important.