The thing is, correction doesn't actually teach them anything.
I would definitely take issue with this, first of all because of my own personal experience learning languages. There were times in my Spanish classes when a certain vocabulary word or turn of phrase was burned into my mind because the teacher had the gall to correct me in the middle of the conversation. But then, perhaps this worked because of my personality--I had a strong motivation to be right, but was resilient enough that I didn't shut down when I had made a mistake. Most of these cases happened in one-on-one situations, though, and not in front of the whole class.
There are many methods of error correction, including giving the student the correct alternative, giving the alternative AND making them say it over right, (the one you mentioned) indicating that there's something wrong and making the student correct him/herself, or simply asking for clarification only when you really don't understand them. These methods have been studied, so there is no reason not to base your teaching on hard and fast research. From what I remember, the most successful method was the one you just described.
However, that method assumes that the students already know the correct way to say it, and that they are just not applying their knowledge. (Be very conservative when correcting beginners.) If they really don't know, you can wait until the cows come home, but they will never come up with the correct form. I try to hold my students accountable only for things that I have taught them. This should be common sense.
Being familiar with the order of acquisition for certain grammatical structures (Krashen has also done some research on this), will help you know what it is appropriate (and useful) to correct, and what is not. But beware: this order is not necessarily the same as the order they are presented in the textbooks.
Peer correction is a great tool
I have found just the opposite. In my experience, when students correct each other, they are impatient and overly critical. And, unlike the teacher, they have no concept of the order of acquisition or different correction methods.