2009's research by internet.com Japan(n=300) told that 12% of Japanese used kana input. 87.7% used roman alphabet typing. Maybe the last person used thumb-shift keyboard, or T-cord.
Roman-type now gets popularity because you remember roman-keys anyway to type English words even in Japanese document, and if roman-alphabet, digits and Japanese are more mixed in text it is faster. But if the documents are mostly in Japanese, and you master touch-type, kana-input users would be actually faster, as the number of strokes will be smaller. There are some known professional writers/bloggers who write for decades and stick to kana-input.
From what I remember of working in an office in Japan: their keyboards are shaped the same as a QWERTY just with hiragana instead of roman letters. Then there is software on the computer that translates typing of hiragana into Kanji, katakana, etc. It's actually quite a seamless experience.
I used to have an iphone over there as well, and texting in Japanese was really easy as Kanji automatically replaced relevant hiragana.
I have a 'Japanese Keyboard' (software) now in the states but it just doesn't work as well.