The Japanese government has a pretty explicit objective in expanding HND's international capacity: they want to make Tokyo more attractive as an international business center and tourist destination, and they think that improving airport convenience is an important part of promoting those goals. The HND expansion is not about, and was never about, making Tokyo more popular or competitive as a sixth-freedom hub. MLIT's website about the Haneda expansion illustrates this well -- unfortunately it's only in Japanese, but it focuses on the importance of improving O&D access to Tokyo without a single mention of competing with other Asian airports for through traffic.

FWIW, HND is physically about 50% larger than NRT, and I believe it will still be larger after the third NRT runway is completed. I also don't think they can significantly expand NRT beyond the third runway without re-settling a lot of people, whereas there is still quite a bit of unused space in HND's existing footprint -- the main constraint at HND is the surrounding airspace and noise restrictions.