I mean, it's true that you might see phenomena that echo natural systems or things, but I suppose what I'm getting at is: unlike natural systems, the "rules" can be changed.
Honestly, what helped me a lot is: Economic systems are more like video games than "nature." Sure, video games can look like nature, but also are extremely malleable.
Genetics however is not only a useful model, it's hard science. You can experimentally find out whether some characteristic is e.g. Mendelian (I'd doubt the greed is, as normally defined).
It got me thinking that to cross the two domains, there is also a meta-concept of cultural viruses ("memes") to which Dawkins applied Darwinian model. Definitely not hard science, but they kind of counter your point that "there's NOTHING natural about our economic systems".