Bitcoin is based on greed, it only works because of the incentives, which Satoshi wrote into it deliberately. And there is nothing wrong with that, greed is instrumental to the working of this dualistic world (we are One, but we are also individuals), to producing value. That's the beauty of capitalism, where the selfish behaviour of individuals benefits the masses (as long as it's done with integrity, with people adhering to certain principles). We have computers, smartphones, cars, air travel, satellites, medicine etc. because we're greedy.
I don't agree with the definition of greed as desiring fair compensation. What is fair anyway? Who decides it? That sounds like the Labour Theory of Value (one bag of wheat is worth two chickens, because some dude or committee of dudes after a day of brainstorming said so), which is a Marxist idea. The Austrian School supports the Subjective Theory of Value, which recognizes that value is subjective and markets are not 100% efficient.
It's human nature to want to get as much as possible for as little effort as possible. If I could choose between:
  1. Getting 1 BTC for a year of hard work
  2. Getting 1 BTC for an hour of easy work
I'd (generally) choose 2. any day. It would seem mega unfair to most, given that millions of people work for $1 a day, but so what? Don't get me wrong; I do feel sorry for them, but I'm not going to pass up the chance to earn 1 BTC for an hour of work just because it seems unfair. And if someone offers me 1 BTC for free, I sure will take them up on the offer. (NB due to the way Bitcoin is designed, with its finite supply of 21M, such an opportunity would be extremely rare.)
Now, some people don't have integrity / principles (which I guess can be defined in many ways, but generally libertarians and ancaps define it using the NAP, non-aggression principle) and for those, choosing option 2. could involve hitting someone on the head with a wrench and stealing their 1 BTC. Or becoming a politician and doing something similar in the name of authority and under claims of legitimacy. And THAT is the problem. Not greed.