The other hive is not a nucleus. It has all the brood frames minus one.
The queen is indeed accompanied by all the foraging bees. Some of these bees revert to wax making but you do not need many of them to nurse brood because you are careful to move the queen over on a frame of sealed brood. The wax makers simply need to keep pace with the queen and are quickly replaced by new emerging bees. The original foraging force stays largely intact to gather your honey. The emerging bees become the nurse bees.
If you nuc the queen she has no foragers to start with and this foraging force will take weeks to build up to strength. Meanwhile the box with the queen cells will have a significant brood break of at least three weeks and often much longer.
Wally shaws modified manipulation achieves the method I described by moving the queen back a week after simply making the whole thing easier if you can’t find the queen and can’t inspect the moved box very often.