Yes. Let's make a lottery based economy. That would boost the productivity and make the nation prosperous. This is like fixing a pothole by creating a supermassive black hole.
Okay, just replace our existing failed welfare system with this then. You don't think there's massive suppressed innovation because so few people can try a startup?
We don't have a "failed welfare system". Welfare works. The only "failure" here is our failure to keep adequately funding it.
It's failed in the sense that poverty rates stopped declining in 1968, when welfare started.