Even textbooks that used to use romanized Japanese for fairly logical pragmatic reasons, like "Japanese for Busy People," which is aimed specifically at busy adults who are trying to learn the spoken language in the least amount of time/effort, have been rewritten to eliminate romanized Japanese! Many people studying Japanese go so far as to consider the presence of romanized Japanese, even in combination with normal written Japanese, a black mark against a book, a viewpoint which I think is a bit extreme.
Additionally, even if there is a benefit to early spoken fluency, it's going to really annoy students when after two years they suddenly have to start learning the writing system from the very beginning. With this approach, students wouldn't be able to use any modern instructional or reference materials for 2-3 years. Basically, they wouldn't be able to study on their own at all.
Also, from the standpoint of practical language instruction, since many students drop out of Japanese classes the second they're asked to learn hiragana (much less katakana and kanji), it is much more efficient for all parties involved to have this occur earlier in the process.
Many people studying Japanese as a foreign language actually also 1) find it very discouraging to discover that they can't read words they know because they haven't been taught the characters, and 2) find it very difficult to parse romanized Japanese since it is harder to tell where words end and distinguish particles/verb endings from nouns and verb stems.
http://languagelog.ldc.upenn.edu/nll/?p=11580
> The problem was that all of my language teachers insisted that I memorize hundreds of characters right from the very start.
For every person who is mad that that they were made to learn kanji from the beginning, there is another who thinks their Japanese ability was permanently impaired by not being taught kanji early enough (I have met plenty of the latter). Regardless of the method, there are people who are going to object to it.