The vision but seems plainly wrong to me, many (and I’d posit most) musicians who have been playing their instruments for years can play with their eyes closed. Definitely would test proprioception though!
Well, those musicians likely have highly developed internal visualization skills, but of course I'm not keen on how transferable that is to real vision.
It's more about muscle memory, touch, and hearing than it is about trying to visualize the instrument in your head.
Source: I'm an amateur musician. Judging that even I can play the instruments I know without needing to necessarily see the instrument or the notes to play (actually or imaginatively), I'd imagine actual professionals shouldn't have a problem.
I'm a trained musician, and what I'm referring to is often called mental play[0]. Einstein referred to it as visual thinking. Many successful experts across many domains will tell you that visualization skills are a key factor in their success.
Any practice routine worth its salt includes visualization exercises. For example, players are encouraged to use mirrors while they learn in order to strengthen their visual memory, and eventually players are taught to imagine the instrument in their head, to imagine practicing. This has shown to be a viable method for making real improvements while not even holding your instrument, including boosting your muscle memory as your body learns to make stronger associations.
I obviously cannot speak for everyone, but when I play music from memory (and yes, often with my eyes closed) there isn't any visualization at all. It's all a combination of sound and muscle memory. Indeed, for plenty of music I would never have seen sheet music to be visualizing...
Visualization is a skill you must develop, a muscle in its own right you have to mentally flex. You don't visualize because you were not taught to, didn't think of it on your own, and thus don't practice it. It's not required for success, but it's a great tool for learning and improving.