I always thought that besides Kanji, one of the most difficult things about Japanese was its immense amount of homophones. For example, 花 (はな), which means flower, and 鼻 (also はな) which means nose. In the sources and books I read, I am simply supposed to tell the difference by context, and this isn't always easy. Let me elaborate:
[Talking to Umami] Your flower looks red.
[Talking to Umami] Your nose looks red.
If I was talking to Umami before that statement and it was clear we were taking about her flower or her nose than yes, I suppose context would help. However, if this was the starting statement, it might not be completely clear. Hypothetically, if she was sick and bringing me a red flower, she wouldn't know from the context and I would have wasted my time specifying that I was talking about the organ or the plant.
Would pitch be helpful or even necessary to differentiate the subject in this case? If so, then why do English sources leave it out? If anything, it should be one of the first things learned, seeing that I basically had to re-learn all of the words I thought I knew how to pronounce perfectly.