In Chinese these are rare exceptions. In Japanese, having at least two (and sometimes four, ten or sixty) possible pronunciations is the rule, and it's the single-reading characters that are rare.
Again, I understand the situation in Japanese, which is why I headed my comment with "your overall point is correct".
And also again, it is not true that Chinese characters with multiple readings are rare exceptions, unless you want to measure rarity by dividing the count of "characters with multiple readings" by "all characters ever attested". Characters with multiple readings are extremely common; one of them, 的, is the most common character in written Chinese by a wide margin.