I'm not sure random draws are even better from a zoomed-out "total welfare" score. People get lot of value from preparing for the future and believing good things will probably happen, especially when it comes to their kids. The random straws outcome makes that impossible. That's a lot of utility to leave on the table.
The flip side is that parents who could not ordinarily build for their kids' futures might feel better. I wonder if that's enough to compensate.