you can't abolish kanji, you destroy almost all compatibility with old documents dating the 8th century as earliest.
That didn't stop Korea and Vietnam from largely abandoning Chinese characters in favor of phonetic writing systems. Anyway, the earliest examples of Japanese literature that wasn't written in Classical Chinese used neither hiragana nor katakana, which renders them almost completely unintelligible to modern Japanese speakers.
Nope, in the same word in hiragana or katakana with different tone may have different meaning.
Japanese has WAY too many homonyms for a purely phonetic writing system to be very useful.
Homophones are typically much, much less of a big deal than people make them out to be. Think about it, if homophones are so numerous as to make a phonetically written language ambiguous, how would anybody make themselves understood when speaking? Context removes almost all of the ambiguity.
Furthermore, Japanese doesn't have a significantly different number of homophones than Korean, Vietnamese, Thai, Lao, Burmese, Tibetan, Hmong etc., all languages that have many homophones yet do just fine with phonetic writing systems. Even Chinese languages can be written entirely phonetically, as the Dungan people do. Now, Thai, Burmese, and Tibetan do have highly conservative writing systems that differentiate words that are pronounced identically in the modern languages. Thai, in particular, uses multiple letters or letter combinations to represent the same sound in order to distinguish words. However, Lao has gotten rid of these redundant letters (Lao uses 27 consonant symbols compared to 44 in Thai, with both languages having nearly identical consonant inventories), yet written Lao is no less understandable than written Thai.