LiveView totally changed the way I shoot astronomical images - for the better. I could never go back to a camera that did not support it (for that purpose, and a few other subjects).
I do a lot of lunar imaging at 700, 850 and 1000mm. For many years I had a manual focus 500/4 Ai-P that precluded the use of AF. In the old days, pre-LiveView, the strategy was to manually focus as best I could, take some shots, and then repeat for as long as I had patience, hoping one set of images was in perfect focus.
The human eye has finite resolution (just like an optical lens or sensor). You eye cannot see the equivalent of the pixel level through the optical viewfinder.
LiveView gives you that pixel level feedback, in real time, without having to shoot and chimp as mentioned previously.
In particular, optically focusing at f/8 (as I did and do to get to 1000mm) is quite challenging and aids like the Katz Eye split prism viewfinder don't work well at those slow focal ratios.
For your application here (wide angle star fields), your D300 should be able to autofocus on bright stars and planets. I've had good luck with that. But I still like to use LiveView, adjusting focus for the smallest possible stellar image.
Autofocusing using stars works increasingly better with longer focal lengths, and increasingly poorer with shorter focal lengths. Somewhere below around 20-35mm it may not work well or at all. Because of that it is a good idea to get skilled at manually focusing stars, and LiveView is the way to go.