I don't understand the reason to learn Onyomi and Kunyomi of the kanji. Do they have any use besides reading out loud? Can't a person just learn the meaning and read?
弥次郎兵衛 is a way of writing the word ヤジロベエ. None of the kanji tell you what this word means. The only way you can tell what it means is by recognizing the word. (It refers to a kind of traditional Japanese toy that balances on a small point, for example in the shape of a dragonfly.)
What if someone's name is 良? You can't call them Good. That's not their name.
What if you see the kanji 百葉箱? This word means "Stevenson screen", but unless you know the actual word the kanji represent, you're unlikely to understand. What's a "hundred leaves box"?
What part of your body is the 盲腸? How about the 虹彩? The 喉仏? The 網膜? The 鎖骨? All of these kanji are used to represent words, and unless you can associate the kanji with those words, you'll have trouble figuring out what they mean.
It's true that you can often figure out an unfamiliar word from the kanji alone. But kanji are used to write the Japanese language, and you won't get very far if you skip the actual step of associating the writing with the language itself. That doesn't mean you have to sit around memorizing individual on and kun readings, but you need to be able to read words if you want to understand Japanese writing.