I think your criticism is a bit misguided. The FDIC insurance fund only covers a tiny fraction of bank deposits and if a single small bank had a run the fund would be insufficient to cover it's customer base. It also covers derivative losses before balance losses, so it's really more of a psychological tool then anything else.

Also banks are investing all of your money in highly illiquid risky assets (aka mortgages) so I don't see how this would ruin the economy or even meaningfully change the risk profile if adopted at a large scale.