I looked at the ingredients I had lying around and thought, what is it about putting them in a wrap actually makes them better? Two reasons came to mind.
One is that it lets unsatisfying scraps create the impression you're really eating something substantial. I cannot quite put my finger on it, but the building up of form and texture that is characteristic of pastry is satisfying in the way something simpler, like pasta with a sauce, is not. I can't help but feel like its addressing the primal urge to eat small animals whole. Maybe thats too vivid? Also, the dumpling withholds its scent until its bitten, making the sensory presentation more intense than is possible with a dish that can be smelled before tasting. In any case, it's a way to turn a little bit of meat or even just vegetables or potatoes into something "big and meaty".
The other consideration is preservation. Making a soup or a hash invites spoilage. Wrap it in dough and especially if it dries out a bit after cooking it will not go bad so quickly.
I had on hand some tired lamb shoulder, some veggies, and so forth, and I set out to make the most primitive possible dumpling out of the worst materials. I cooked the lamb quite a while, unfortunately scorching it a bit more than I had intended, along with onions and various veggies. For the dough, I made a very soft pasta dough and rolled out small pieces into circles with quite a lot of flour. This was easier than expected. I've seen Chinese chefs do this on TV at a rate of about twelve a minute, which looks like it takes a lot of practice, but I was able to get the basic roll and turn motion down so that I could roll out most pieces efficiently without having to touch them directly. Without aiming for accuracy or a particularly high filling to dough ratio, I made a bunch of rough looking lamb filled dumplings, boiled them only briefly, and stuck them in the fridge. I didn't want to actually test non-spoilage the hard way, just get a sense of how they aged.
Even after a couple of days, when retrieved from the fridge and pan fried, they were pretty good. Even though I made them deliberately "badly" their appearance magically improved during cooking. Don't plan to do this normally, but thinking about life without machines and refrigeration gave me a better sense of the motivation behind this technique. Next step, I am going to apply these insights to some more traditional pork potstickers, one of my favorite things in the world. This time around I think I can get improved results - rustic looking, simultaneously chewy and tender and juicy and crunchy, and intensely flavorful. And maybe not have to cook for a few days afterwards. :-P