Nagi is 13, Kousei 14 years old. Nagi is a bit childish by style and behavior, but if she revamped herself, wouldn't she actually be quite similar to Kaori? She has the spunk, certainly, and also, perhaps equally importantly, the good looks. She was only Kousei's student because she isn't as advanced as a pianist and because Hiroko was crafty enough to make Kousei teach her in order to expand Kousei's circle of friends/acquaintances. By getting together with Nagi, Kousei would also gain Takeshi as a brother-in-law, which means those two could compete more intensively as they would probably communicate and meet more often. I reckon the Aiza family must be somewhat music oriented, which could help Kousei as well during his early career. It didn't seem like Takeshi would object either, as long as Kousei would keep rocking the piano.