As a childless single person - Why should I have to deal with other people's screaming kids in public. If the parent does something, thats fantastic, but lots of parents just let them scream or even worse, they placate them with rewards for bad behavior. I work at a mass retailer and I am always annoyed when parents let their children walk around bother employees instead of keeping them with them (which is really safer) It is not my job to entertain someone's child while they shop. If a company wants provide me with child free shopping times, I'll take them. After all, these are actions ultimately done at private business establishments, not government buildings. The only reason this is happening is because its lucrative business wise.
And on your take Savage Idealist - Its not my place to offer advice to parents. They tend to get offended. Especially those who could use it the most.