I think there are two major categories of situations where a correction is needed. Times when an excepted behavior is not taking place ("Clean up that mess") and times when an unacceptable behavior has already taken place (Sibling A hit Sibling B).
In the first case, emotions may not be that high to start out with (and my never get that high). The timeout is a "self-inflicted" punishment that lasts until they do what's expected of them. There are certainly times when the "Do a thing!"/"No!" loop has spiraled out of control, and in that case the timeout first serves as a cooldown, then a conversation can take place laying out the expectations more clearly.
In the second case, tempers have generally already flared. There is generally an action that needs to take place in the short term ("Apologize to your brother"), and there generally needs to be some sort of punitive consequence. In that case the timeout a) gives tempers a chance to cool, and b) serves the same self-inflicted punishment as before ("You're going to be in timeout until you apologize to your brother"). The other (major) benefit is that it buys time for me to decide on an appropriate punishment outside the heat of the moment.
> There was a german parenting TV show a few years ago where the host repeatedly made children of various parents sit somewhere alone until they cooled off.
I'm not a huge fan of being "alone" as a punishment. For me the concept of "timeout" and "alone" are two separate things. There may indeed be times when being alone is what the kid needs to cool down before they can talk (my daughter is absolutely this way), but I think it's important for that to be their choice (and it's equally important for them know it (can be) an acceptable and healthy choice). For other kids (like both of my boys) being alone is just going to work them up more. I generally spend the first few minutes of a timeout sitting right next to them (or with them on my lap) until they have been able to calm down and we can have a conversation.
It's probably also important to note that we're all just talking about the "ideal" here. I'm sure none of us meet our own ideals as consistently as we'd like...