I think, in a way, the different answers on this thread should give you a pretty clear answer: it can be useful for some people, but is in no way necessary. No matter how many people make the argument that they think learning on / kun is ‘as important as learning your abc’, so long as there are some people who are doing okay without that knowledge, it proves that it’s not necessary.
I’m by no means an expert in Japanese, but I’m doing okay. I have no idea what the on / kun are for even one kanji. I have never tried to learn and don’t intend to. However, so long as I know what the potential readings are, I can guess which one to use in most new words with a very high hit rate.