Lots of interesting thoughts here. Like most people here I also use both methods. I've sung as long as I've talked so learning from written music came second.
At primary school in the 1950s, in Australia, we were given ear training alone -- a cheap option and very effective. We were shown how to find intervals by using well-known songs. We sang a lot. In high school we were taught to read music AND how to combine it with singing by ear. Again a cheap, but effective, option. There was no money for instruments for every child. Piano was used because you can easily see where the notes are -- even when it's just a picture of a keyboard.
We were very lucky -- I believe. My children and grandchildren were/are not so lucky -- Sad.
Cheers, Joy