The Kamui-worship makes sense in this game when you consider the traits about the character:
- Royalty in both kingdoms
- Noticeably different in appearance (pointed ears, white hair, can turn into a dragon)
- Possesses legendary sword that literally chose Kamui as its owner
- Has a peculiar history that makes him/her stand out from the other siblings (stolen from Hoshido, imprisoned in Nohr), giving both families reason to pay special attention to him/her
Those are more than enough to achieve what is basically celebrity status. In addition the story portrays Kamui as someone who is easy to get along with, explaining why the neutral characters are so devoted to him. Obviously this is all meant to serve as wish-fulfillment, but it's wish-fulfillment that works as much as some people might dislike it. I know more than a few people that hated Frederick from Awakening simply because he had the audicity to be cautious of Robin, so it's no surprise to see it carry over to this game. It's also the same reason why we still have waifus/husbandos, marriage, children, and fanservice. It works.
I mean, a change of pace by going back to no more self-inserts would be nice, but I can't see IS being too willing to change a forumla which is clearly working out for them.