Is music reading an important skill?

That all depends on your definition of important. It is certain that playing music is a much more important skill for a musician.

Music reading can:

Allow you play music you can't hear.

Allow you to quickly communicate music to others who can read.

For many, learning to read music is accompanied by an increased understanding of music theory (as in, what chords will likely sound good at different places in the melody?)

If you are doing arrangements, it makes it easy to visualize how everything lines up and which harmony or counterpoint notes might sound good with the melody notes.

On the con side, many of those who have been trained extensively at reading music find it difficult to learn to play by ear.

None of this has anything to do with the skill of the player or with what the music sounds like.