> You would have to invent a system where pitch accent could be indicated for each word

Really not hard to do. A symbol on the syllable bearing the pitch accent would solve the issue

> And then there are the words with little or no pitch accent difference, only context

What's happened is that effectively a written "shorthand" has emerged that has evolved somewhat separately from how people speak. Losing kanji would mean losing this shorthand, in favor of writing more closely akin to the way people actually speak, but this is how the vast majority of written languages work. Preserving this shorthand seems like thin gruel to justify the complexity of kanji.