The biggest reason to do this is that I can play with my right hand while drinking beer with my left. It's what makes the mandolin a truly great instrument. You can no more do that with a fiddle than you can sing and play pennywhistle at the same time.
"What would you pay? But wait! There's more ...." Droning also helps get you pick control. Drone a few tunes and you'll have demonstrated to yourself that you can find the string you want, without looking. You'll have a heightened sense of where each string lives.
Ear training is yet another advantage. Playing a strict drone through the tune, like the banjo, is sometimes discordant. Discordant is interesting, but with four open strings it isn't your only option. When you're in D, G, or A, you have an open string in every chord available, so there's a guarantee that you can find an open string that fits, changing strings as the chords change.
It helps your rhythmic sense, too. Without notes, you're a drum. (Okay, okay -- if you're changing strings occasionally, you're a set of tympani.) Don't believe playing a mandolin like a drum makes sense? Bruce Molsky says he thinks of his fiddle like a drum,
If you're really not convinced, go find a Hungarian band with an utogardon.
The utogardon looks like a cello from the Bizarro world. It's roughly carved, from a single block of wood, and has four strings, tuned to D, D, D, and ... D. (Not all the same octave.) Instead of a bow there's a stick. The legend is that a Transylvanian peasant, walking down a road, came upon an abandoned cello. Perhaps it had fallen off a cart. Perhaps someone had thrown it away in disgust. He took it home and, never having actually heard a cello, assumed it was some sort of elaborate, amazing, rhythm instrument. Once you've played in a jam with one, you'll know he was right.
I've danced contras and squares to everything from oboes to digeridoos, but never yet an utogardon. And I want to.
Droning is good accompaniment. It sounds dopey on guitar -- I've tried it -- but if there's someone playing a solid melody, it's an interesting, other, mandolin backup style: neither chords nor harmony, neither melody nor counter-melody.
Watch a beginning guitar player watching someone who plays really well. Dollars to doughnuts, they'll be watching his left hand. If you see someone watching his left hand, too. When you first start to play, finding the notes seems like the big challenge. Doing away with your left hand opens you up to the world of possibilities in your right. Playing this way from time to time can make your two-hand playing a lot more interesting, and help move you away from the focus on fretting and ornamentation that's consumed you since you first picked up your instrument.
