So, what does the suffix '-ician' signify?

Merriam Webster: "specialist; practicioner"

Yourdictionary: "a person engaged in, skilled in, or specializing in (a specified field)"

Other examples are magician (specialising in, or practising, magic), beautician (specialising in, or practising, beauty), mathemetician (specialising in, or practising, mathematics), etc., etc.

So, a musician is someone who specialises in, or practices, music. Not just instrument playing.

An instrument player should therefore be called an instrumentician.

... or maybe an instrumentalist!