It also depends on the student/teacher match. I took piano for many years as a child. Unfortunately, I had a teacher who was firmly an advocate of the Suzuki method. The Suzuki method is a good method for some students that highly emphasizes precision. Songs are played over and over again until they are rigidly precise. I do not necessarily have an objection to this in principle, but for myself, I have a very small "twitch" in me that is normally wildly subclinical, but makes it very difficult for me to hold a rigidly steady beat for more than a minute or two without a twitch showing up. Even by the standards of music this normally wouldn't mean much, I never even noticed it playing trombone in band, even marching band, but in the Suzuki program it meant I was stuck playing Twinkle Twinkle Little Star in a variety of rhythms for what looms in my memory as years. I don't know how long it actually was, but it was way too long; by the time I moved on, I could only play sheet music in C, a crippling blow for a pianist.

Or, so I thought. A couple of years after I stopped formal lessons, I started composing on keyboard, and was deeply shocked to discover that when I was doing my own thing, I had no problem whatsoever playing in the key of my choice. It turns out that if you play enough scales for a given key, you can play in that key just fine.

Nevertheless I never did develop the ability to play sheet music in arbitrary keys without a lot of work constantly going into remembering the key.

I would have done a lot better with a teacher that figured out the Suzuki method was a poor match for me. Or if I had had enough knowledge to figure that out myself.