Leashes for Children: Yay or Nay?

These little guys are everywhere: airports, grocery stores, parks, etc. While it can seem understandble (who wants to lose their little one?) it can also seem a tad on the crazy side. Can you ever help but not picture a dog every time you see a kid trying to run from their parent...only to be held back by some fabric?

So what do you think? Should leashes stay off children in lieu of a pet? Or is it your choice of safety?