This is a common misconception (which I shared until I studied Japanese).
Writing a sentence may be more of a hassle than with an alphabet based system - and even that would remain to be seen - but reading it is much more efficient due to the more condensed form factor: a page of kanji would take much more space written in romaji.
The fact that Japan and China stuck to an ideogram-based writing system did not stem from a lack of alternative. Japanese actually has had not only one but two syllabic alphabets for more than a millenia (1). Yet kanji were kept, notably because of the numerous homophones in the Japanese language.
(1) http://en.wikipedia.org/wiki/Hiragana#History http://en.wikipedia.org/wiki/Katakana#History