There are 14 homonyms for そうかん -
「そうかん」の検索結果 - Yahoo!辞書 - and that's just in the freely available dictionary, 中 dictionary and on my first stab. All I need to do is and match pronunciations in two parts from common readings かん、けん、かい、けい、そう、さん、しゅう and I can usually find a (long) list of homonyms. The scale doesn't even begin to compare to for/four or to/two/too.
Given sufficient context, of course the words can be distinguished without kanji. However, I think you'd find that when quoting small excerpts of written works even natives won't be able to straight out understand it - although the person doing the reading will likely recognize an ambiguous situation and provide a clarifying comment.
Of course Japanese was spoken before there was a written language, but -that- Japanese didn't have on-yomi compound words in it. Aside from the homonym issue of these words, the kanji act much like greek and latin roots in English - they are one of the keys to learning a word in context by how it's written. Remove the kanji and now you've got nothing but senseless homonyms with such short pronunciations that you can't really get any 'root word' clues.
That's why I say, if you forced people to do without kanji they would drop many sino-Japanese words in favor of older words or loan words from non-kanji languages. Without the kanji the words will just be difficult and have to be qualified and described all the time and in a natural language that kind of difficulty is quickly smoothed over by a change in habit... especially when there are greek, latin, and english loan words for all manner of technical terms anyway. Maybe new native words would be coined as well, who knows, but -something- would have to give.
So yes, you -can- communicate in -a- Japanese language without kanji, but adding kanji to the language drastically changed it and taking them away would drastically change it again. The language -as it is now- needs kanji.
I disagree that adding particles to words when spacing them is a mistake, as well. One of those native japanese homonyms that's rather famous is 橋・端・箸 （はし) - but these cannot all be distinguished audibly until you put them in context. In context, the pitch-accent 1 and pitch-accent 2 word become different because post-position particles take on pitch-accent relative to the word they attach to.
Theoretically, we could consider post-position particles a form of declination, and treat them as part of the words they attach to; it's just that the current way of looking at them involves a lot less cases to actively memorize. It doesn't make them any less tightly bound as a word unit to the word they follow - witness how even in strange sentence inversions and reorderings the particle sticks to its word almost like it was part of it. I find separating the particle from its word strangely unjapanese and harder to read, personally.
