Nah, kana take up way too much space, and with no spaces in the language that makes parsing kana only text a lot slower than kanji.
On top of that, the language itself is phonetically very simple, so if you didn't have kanji there would be way too much ambiguity in written text, which is already very differen from spoken Japanese.
Now, if Japanese invented a new Korean style alphabet that combines sounds into a single character, and introduced spaces to the language then I could see it working, but I don't think most people would want that.
But that's true as much of modern Japanese as it was of Korean before they dropped Chinese characters, or of Chinese before the simplification of Hanzi.
Eventually, people would just get used to a new way of writing things and be able to absorb that quickly and efficiently.