What you're thinking of isn't tribalism or subsistence economics but actually a post-scarcity economy, one in which resources are so abundant and easily acquired that there is no need for money or trade. This does not necessarily imply anarchy in which there is no ownership, but it does lend itself to that.
To an extent, tribal societies did live in something like a post-scarcity environment. Some didn't have a strict concept of personal ownership of goods and many didn't believe that it was really possible to "own" land, but that doesn't mean that things weren't "claimed", for lack of a better word, by groups or individuals. For instance, even though an area of land might not be "owned" by any particular tribe in the way we would use the word, it could still be regarded as their territory in that it would be seen as disrespectful for another tribe to use it or try to take its resources. The same goes with physical goods. This was the case because often resources were so abundant that property rights didn't need to be strictly enforced, but they did have economies and systems of trade, just not ones we'd be familiar with.
Aboriginal or Native people are just as human as anyone else and therefore just as prone to greed, but because they live in very different cultures and have very different material interests it just takes a different form than what we usually think of. It's unrealistic to try to spin it as a fall from grace myth where everything was wonderful, pure, and perfect until the corrupting influence of evil came along and ruined everything.
Honestly, no, I wouldn't want to live in a tribal society, but I would like to live in a post-scarcity society where I could worry about things besides what meaningless toil I'm going to need to do this month to pay my bills.
