Earlier this week, I went and set up a certificate of deposit. It took half an hour, making arrangements to visit on the rare day their hours didn't clash with mine, presenting two forms of identification, and having a significant amount of money to contribute to the account at once.
I also bought a Powerball ticket the same day, which was a $3 commitment and took 20 seconds at the all-night Kwik-e-mart I was already visiting.
Yeah, people keep coming up with various gimmicks (apps, automatic transfers, rounding up your purchases) to encourage saving, but that still targets an audience fairly high up the curve-- people with savings accounts or at least bank relationships already.
If you made a product reminiscent of the UK Premium Bonds, made them a bearer instrument (to minimize friction in purchase, no account or KYC stuff needed), and sold them in every store that offered Lotto tickets, you'd have a product which could get a lot of people onto the savings bandwagon. You've got $10 to put away? You're undocumented? You're 12? No bank will touch you, but you can start squirreling away these bonds, and in a few years, have a nice little nest egg, even if none of them pay out.
Those are government bonds, but it's not far off your idea.
Edit: for clarity, the effective rate paid does vary over time according to interest rates, which usually have some relation to how well the markets are doing.
Uh, maybe? There is a positive correlation of sorts, but it's nothing to write home about. It doesn't seem like this product was designed with any attention to the potential of better-than-fair payouts.
At least in theory, this seems like a great idea. Potentially ripe for abuse, just like a lot of lottery systems (eg. the McDonald's Monopoly conspiracy where employees hoarded the winning tickets).
Hopefully the law can be changed enough to start a larger sized trial.