>What little money they have doesn't get invested, but spent frivolously.
The implication you're making here is that these people wouldn't mind losing $500/year, because it's otherwise being spent "frivolously". I don't think this is true because if you're spending it on something, you're getting joy out of it, otherwise you wouldn't be spending money on it in the first place. For reference, $500 can buy you a game console or several games, which can provide you with tens or hundreds of hours of entertainment.
If it's really the case that the $500/year is being spent frivolously (ie. being spent on things that don't bring joy), then the correct course of action would be some sort of intervention that forces them to save, so they receive a large enough lump sum that can be used productively. We sort of see this happen with tax refunds, where people are basically forced to save throughout most of the year, the IRS gives it back at the end of the year, and they spurge the refund on a big purchase.
>Doesn't it make sense that the utility curve is convex, not concave - that $500,000 is more than 1,000 times better than $500, when compared to $0?
What makes you think that? I think it's generally accepted that money has a diminishing returns on happiness. I guess if you go to the extremes there's some ranges where it doesn't apply (eg. it's hard to do anything fun with a $5 bill), but there's also nothing preventing you from saving up the money.
>After all, suppose that $500 was a year's spare income. Even saving for most of a lifetime would only yield $20-30,000, nothing like enough for many of the opportunities that half a million would make possible.
You're off by a factor of 2. Factoring in a 6% inflation adjusted return, you end up with a return of $77,380 if you do this for 40 years.