I'll say first that I found the existence of that button thanks to this post. The tutorial says nothing about it, and it is very dark when not possible to use it -always at the begining of each turn, so it should not be surprising some new players like me might not notice it-.
Now that I'm aware of it, I've found a very interesting use: when I want a new town, save many AP and then I build a long bridge of tiles, and then undo untill the optimal distance for the town. That way, I save a lot of time instead of having to add tiles one by one, then go to town center and see if it is settable or not, then go add another tile...
Apart from that, it is unusual I use it, because I think carefully wich building/action next. But I guess that once I start automaticing some buildings process, I will make mistakes and having that button will be sweet.