The "many pronunciations for one kanji" thing isn't a problem in practice, because 1) most kanji have _1_ on'yomi (Chinese) and _1_ kun'yomi (native) pronunciation, with it being obvious which one to choose from context, especially because when it's kun'yomi, the kanji are suffixed with hiragana to denote its correct pronunciation. There are however problematic kanji, such as the one you note, because there are several things it could mean, but this isn't really any different from _all_ languages.
Given any sentence, there are multiple possible meanings, and we have to disambiguate depending on context. This is true even for sentences like "The man is here", which man?
The part about complexity is less "ambiguity", and more "how much headspace do you need for the language". I'm not sure if Japanese is more complex than English in that regard, but I do want to note that 1) pronunciation is very straightforward 2) it's *very* hard to make spelling mistakes 3) there are very few irregular words.
Especially point 2 is quite important IMO. If you look at rates of dyslexia, you'll see that they're much less in countries that use Chinese characters. Interestingly, many Japanese people whom I know, who have no issue spelling in Japanese, show the very common signs of dyslexia when spelling in English.
I think it's related to there being fewer ways to "fuck up". In English, it's easy to mix up the letters, transpose them, etc.. With Chinese characters/kanjix, _you can't transpose strokes_ digitally. There are people who make mistakes when writing by hand, but even that is much less when writing kana, the reason being that while in English, "relatiounally" and "relationally" might be similarly, transposing whole kana changes the pronunciation such that it's entirely distinct. Transposing strokes within a kana is of course still possible.