You are imputing human characteristics onto a political-economic-social system with it's own internal rules and laws. It's not "greed". That's a human failing. The system doesn't give a rat's ass if you're greedy or not. It does, however, work BETTER for you if you are greedy.
And this "If we had real Capitalism...". This IS "real capitalism". The more unfettered and unregulated that capitalism IS, the more it defaults to it's basic internal rules and regulations. In this I agree with the Freidmanistas and the neo-liberals. "Real capitalism" doesn't care about "people at the top caring about people at the bottom". Real capitalism cares about one thing and one thing ONLY. To make as much profit as possible. Anything else is an accidental byproduct.
The only times when capitalism can work for "everybody" is when there is plenty of room to expand and plenty of resources to use for that expansion. Then the value of an individual's labor power goes up because there's plenty of jobs and, by the laws of the system, capital MUST PAY FOR THAT LABOR POWER. Or lose potential profit. The days of plentiful resources to fuel plentiful expansion are over. In today's world the only way to expand for capitalists is for them to take over OTHER capitalist holdings. And resources are running out which also provides a check on any growth potential.
The age of capital is over, it just doesn't want to admit it. Capitalism WILL fall relatively soon in an historical perspective. It's just a question of how many it takes with it WHEN it falls. We are rapidly approaching the "socialism or barbarism" stage. I know which side I've chosen.