When you take into account Natasha Yar's childhood where she grew up in poverty having to hide from rape gangs then is it even really post-scarcity?

Or is it just post-scarcity for Starfleet and certain parts of the Federation?

Turkana IV (Natasha Yar's planet) started off as a federation colony after all. And became a dystopia even while still a member of it. So if the Federation is considered a post-scarcity society then why didn't Turkana IV benefit from that?