Are these mutually exclusive?

As someone who enjoys music, from punk to jazz, I wish I could identify a C from a G as easily as I can identify blue from green.

We’re taught to use our eyes to identify colors, why not teach children to use their ears to identify notes?

Colors are useful. Perfect pitch is pretty much useless. The exception being a composer or school conductor (you really gotta scold those children, haha). While it is a fun trick to have, the practicality of it is very different from knowing what different colors are. The most useful application of perfect pitch I’ve seen is my high school orchestra teacher honing our intonation.