Using the Latin alphabet in no way means "buying into the idea that each letter has a particular pronunciation." This is very obvious if you speak Irish, but even in English there are phonemes that are written as digraphs (most obviously th but also ch and sh - which is why Hepburn seems non-awful to people whose native language is English) - no Latin orthography that's in live use as a spoken language is, or could be, "consistent" in your sense.

The 50音表 regularity is real and meaningful (e.g. it shows up in verb inflections); any representation that lacks it is necessarily less faithful to the native experience. Whereas the letter-sound correspondence in Hepburn is not consistent in the first place ("chi" for ち is ridiculous to anyone who speaks a non-English language), so the idea that Nihonshiki is somehow less consistent is simply wrong.