I am interested to see where this goes, so subbing...but I want to guess an answer
I think the nutrient will be consumed in the starter - it may accelerate the process of building up the volume of yeast, but won't result in more yeast being produced. It just gets you there quicker. But because of the volume of what you are working with, its not critical. Once the starter is done, you will have a good volume of yeast, but it won't have nutrient in it because its being consumed.
Whereas if you put the nutrient in the wort, it will help kick off the fermentation a lot quicker and gets you a much better/healthier ferment than if its not present. At that volume the nutrient makes a big difference to the fermentation - gets the momentum up and the beer to FG quicker.
So I think its better from a fermentation perspective to throw the nutrient in the wort while its cooking, also less risk of infection that way (although you can boil it up before putting it in the starter).
Even when I use a lot of yeast (when recycling), there is a notable difference in the speed and health of the fermentation between when i add nutrient and don't.