I do not believe the getting rid of Kanji would be a good idea. For many reasons already stated, like visual recognition, ease of separation between words and particles etc.
I believe people who argue for the abolition of Kanji using the "hey look at Korea" argument, may have some flaws in their reasoning.
Now I do not know very much about Korean, so I could be totally wrong here, but my first assumption would be that the abandonment/phasing out of Hanja (Kanji) had less to do with smoothing out education, and more to do with national pride and political issues. Therefore using Korean as a prop for the "make Japanese language education easier" point of view does not necessarily hold much water.
My second argument is that Korean and Japanese are different languages, yes they have their similarities, but just because something might be working out for one, does not mean it will just magically work for the other.
Now I do not know Korean, so I can only argue with what I have observed so far about the language.
Hangul and Kana, are not really comparable as writing systems. Just looking at Hangul you can tell it is more complex and allows for greater distinction in pronunciation and word formation. As this next quote explains:
"The organization of Hangul syllables—with individual phonemes clustered into a syllable, rather than organized in a horizontal line as in English—is thought by some observers to be a powerful reading aid. Because of the clustering of syllables, words are shorter on the page than their linear counterparts would be, and the boundaries between syllables are easily visible (which may aid reading, if segmenting words into syllables is more natural for the reader than dividing them up into phonemes). [25] Because the component parts of the syllable are relatively simple phonemic characters, the number of strokes per character on average is lower than in Chinese characters. Unlike syllabaries, such as Japanese kana, or Chinese logographs, none of which encode the constituent phonemes within a syllable, the graphic complexity of Korean syllabic blocks varies in direct proportion with the phonemic complexity of the syllable. [26] Unlike linear alphabets such as English, the Korean orthography allows the reader to "utilize both the horizontal and vertical visual fields"; [27] finally, since Hangul syllables are represented both as collections of phonemes and as unique-looking graphs, they may allow for both visual and aural retrieval of words from the lexicon."
Wapedia - Wiki: Hangul.
In short Hangul is much more effective as a stand alone reading tool than Kana is. Therefore purging Kanji from Japanese would most certainly not enhance its readability based upon these observations.
Last I would like to comment on the "Kanji doesn't fly out your mouth when you talk argument". I do not see how this is really a practical argument. Verbal comprehension and reading comprehension are totally different skills, or were all those language classes we took in school to help us learn to read and enhance our ability just an illusion?? There is a reason formal edjumucation was started.
In addition, spoken and written languages can sometimes be totally different can they not? Japanese constantly omit particles and shorten words when they speak. And lots of times there are many words that are just typically not used in spoken language. So I just don't see how saying that because people can verbally understand each other without Kanji, removing Kanji from the written language would necessarily be a good thing, or acceptable.
I know that many new learners may feel that Kanji is the bane of their existence, but patience and practice will payoff someday, and you will see that Kanji is your friend and probably the greatest tool the language has to offer you in helping to improve your reading comprehension and vocabulary.