They are very reasonably separable. If they weren't, countries like Korea couldn't have switched their orthography (which they did).
Also Japanese people enjoyed playing games like マザー2. This is part of "actual native media", and Japanese writing could look like this:
https://youtu.be/F_UrqsO2JQ0?t=10m15s
(Notice the native narrator has no trouble reading the kana-only writing.)
It's true that much of current native media still uses kanji, but they aren't "immediately necessary". There are books/manga with furigana and software tools like Rikaichan/kun for online articles.
People should be able to learn whatever they want outside of the classroom, including kanji (being able to recognise commonly used characters certainly helps in understanding native media). It's just that grammar, vocabulary, etc (real language) are much more important than kanji for beginners.