If we take Picard at his word, the desire to accumulate "luxury" items is simply a thing of the past.
PICARD: That's what this is all about. A lot has changed in the past three hundred years. People are no longer obsessed with the accumulation of things. We've eliminated hunger, want, the need for possessions. We have grown out of our infancy.
Now admittedly, there will presumably be (mentally unwell) people who want things that can't be provided through replication or through public lottery. It's fair to assume that they would simply be told "Sorry, you can't have your own island" and given the contact details of a counsellor who can help them deal with their issues.
That being said, it would appear that humans do occasionally want things that have uniqueness value, in this case Jake wants to buy a present for his father at auction.
JAKE: Hey, watch it. There's nothing wrong with our philosophy. We work to better ourselves and the rest of humanity.
NOG: What does that mean exactly?
JAKE: It means. It means we don't need money.
NOG: Well if you don't need money, then you certainly don't need mine.
It seems unlikely that Jake would slump into a deep depression if he didn't get it though.