"The advantage of LiveView is that you can enlarge part of the picture and see whether you got rid of the star trails." ...and you can use the enlarged view to confirm focus. Many (most?) lenses are not really focused on infinity when you center the infinity mark or put the focus ring against the stop. In fact, many telephoto lenses specifically allow moving the focus ring beyond infinity to allow for thermal changes in the lens (it lengthens when warm and shrinks when cold).
To confirm focus when I use my D200 I have to take a shot and then review it at an enlarged size afterward - not as convenient as live view.