There are big polemics about how mouthpieces should be shaped. I know why our mouthpieces are like what they are like. And maybe that’s also what you like ;-)
The size of our mouthpieces is between ø28mm and ø36mm, mostly between 30 and 32 mm. The size depends on the size and depth of a particular instrument. The bigger and deeper it is, the bigger the mouthpiece.
All Duende mouthpieces have a thin rim. They are between 1 and 4 mm, and average about 2,5 mm. Their edges are relatively sharp. Not sharp enough to cut yourself, but sharp enough to feel the mouthpiece well. It is so thin to gain better control of lips. It is especially important with lower keys, when one needs to be able to sufficiently relax lips. If the rim of a mouthpiece is thick, it blocks and prevents lips from moving in an adequate manner.
Thus the main reason for these relatively large diameters and precise shapes of mouthpieces is to be able to produce the drone easily.
Another reason for relatively big mouthpieces is that the ability to make articulation, fine expressions, texture changes, comes with involvement of larger area of lips. Otherwise, it is (nearly) impossible to distribute separate tasks on different sides of lips, for example. And one is hardly aware of the different parts of lips playing if they do not have enough space.
There is another reason for the moderately big and thin rimmed mouthpieces. In parallel playing, due to many different techniques coming together, especially fast drone and toot exchange, a player makes a lot of playing grimaces. When you squeeze the 6th toot, you probably stretch your lips a bit, and if you want to instantly fall to the ground tone which is more than 3 octaves below, you have to momentarily relax your lips and bring them to the right position. If you have some friction between the mouthpiece and lips, the lips can get “glued” to the mouthpiece in this split second and end up in some distorted position not permitting you to hit the drone on time. In reaching the perfect form, one is to avoid events like this.
This is why Duende makes didgeridoo mouthpieces like it does.