I feel this is really beneficial to have a list for in my studies. The reason is if I see an unknown word that I'm reasonably sure has onyomi readings, if the kanji in question have only one possible reading, I can automatically read the word. Score! But if there are multiple onyomi per character, I'm going to have to consider which reading applies. Single onyomi Kanji make for smooth reading and learning.
As for the multiple-onyomi Kanji, I'll be wanting more careful practice, so I'd like to know the list of them.
I could find all this out manually by looking up thousands of characters, but is this a known thing?