The "paying the babysitter" scenario was the one I conceded was easier in the EU than the States. It would be nice to have such functionality here but I hardly feel like I'm living the dark ages for not having it. It goes one of two ways:
1) She gets cash. This is usually the preference in the States for such transactions because it's tax free income. I certainly prefer cash for the various side gigs I have.
2) She gets a check. Funds are available next business day 99% of the time.
As I said, it's not as sexy, but it gets the job done. Person-to-person payments are pretty low on the list of things I'd fix with regards to the American financial system. And yes, there are problems with paper checks, and they should go away, but on balance there's not a lot of fraud being committed with them. The bigger fraud issue is cloned credit cards, which I did point out. :)