In an all-grain, all malt wort, with only 1 generation of yeast, I'm not sure there is much of a reason to use nutrient. The main reason to use nutrient is to extend the health of the yeast into another batch. Otherwise, it can get "tired" in just a few generations.
Using nutrient in a starter is sound, because starters tend to be low gravity and you want to build up yeast sterols for the main event.
I think some nutrient in extract and partial mash batches is a good idea. Without it, I've seen a lot of incomplete fermentations. Malt extract just seems to have some portion of nutrients stripped out.
Nutrient needs to go into the boil because uptake is at it's peak at high krausen. Once primary fermentation is over, the yeast has already prepped itself for dormancy.