Regarding learning by ear vs. sheet music: This is a complex issue and both sides have their purpose.
I think that if you look at the oral tradition vs. printed books, you can see a parallel to learning music orally or by written sheet music.
The oral tradition although it could be epic in length, used repeated rhythm and rhyming patterns to help people learn the story/poem/legend/etc. Written words allowed authors to break away from those patterns to produce more complex written styles. Although not impossible, it would be hard to memorize a novel by Tolstoy or James Joyce.
I play in a symphonic orchestra, and cannot even imagine trying to learn a symphony by ear. Yes, it could be done, but it is much easier to read the music. When you have lots of different instruments and complex arrangements, sheet music allows competent musicians to play together without even having heard the music before.
A good classical musician will hear the written notes in their head while reading music. It's very internalized after years of practice. I've been playing my secondary instrument (euphonium) a lot at home the past year, but I noticed how my body doesn't react as instinctively as when playing trombone. With trombone I see the note, my arm moves without much conscious thought, my lips buzz the pitch and the sound comes out. With euphonium, my fingers aren't as automatic as my slide arm. So although my lips are ready with the pitch, my fingers can get tripped up or delayed. LOL. The same should be with dulcimer playing, although dulcimer has the added complication of different modal tunings, so the brain and body need to learn them all.
When you look at the folks tales and folk songs versus books and classically written music. You see where the the author/composer's intent has little with the former, and each reteller/resinger creates a new version but within the tradition. The stories are songs are truly the people's. With books and symphonies, etc., you can interpret what the author meant or how the composer wished the music to be played. Even if readers and musicians can create their own interpretation of the works, the creator of the original is very much at the heart of the work.
Learning folk music should lean more heavily on the oral tradition (with the help of sheet music and recorded music for those that need it in the beginning), just as classical music should lean more heavily on the written tradition (with help from a good ear and hearing other musicians playing the piece).
When my first child was born here in Sweden, I started looking for American folk songs to sing to him. There were no American folk singers around in Örebro to learn from, so I ordered a book from the Internet, played the melodies on the piano and sang along. Then I started hunting the Internet (then via Napster LOL) for recorded versions of all the songs. I started singing without the sheet music (hard hold a music book while also holding a crying baby), using my ear to create my own version of the songs, mixing the various versions of lyrics and playing around with embellishments. So it was a mixture of sheet music at first for the new songs (or to refresh my memory for songs I heard/sang as a child) and then a healthy dose of playing by ear and experimentation.
So neither side should look down upon the other. Great musicians can come from either tradition.