Not closer to the spoken sounds, closer to English orthography.

I don't know the details history of the system's development, however I notice that with Kunrei everything spelling is neatly 2 characters while with Hepburn it may be 2 or 3 characters:

Kunrei: ki si ti ni hi mi

Hepburn: ki shi chi ni hi mi

The politics of the issue is obviously that Hepburn is older and an American system while Nihon and Kunrei are very purposely domestic (Nihon "is much more regular than Hepburn romanization, and unlike Hepburn's system, it makes no effort to make itself easier to pronounce for English-speakers" [1]). Apparently, Hepburn was later imposed by US occupying forces in 1945.

Perhaps 80 years is long enough and suitable to effect the change officially with no loss of face.

[1] https://en.wikipedia.org/wiki/Nihon-shiki