The Caldera Cone is sort of a darling here because it is one of the more efficient alcohol setups. (I'll save the question of why alcohol setups are particularly popular here for later.) Also, a lot of people just think that it is inherently cool to have a windscreen that doubles as a pot support. The Ti versions are also incredibly versatile, burning alcohol, Esbit, or wood.
But probably most importantly, the Trail Designs skunkworks put a LOT of R&D time into their stove to ensure that it would work well in the widest possible spectrum of conditions, elevations, fuels, wind, etc. Thus, as alcohol stoves go, the CC is one of the more user-friendly ones- which you already know if you have ever struggled with an aluminum foil windscreen in a high wind. You can't really say that of a Fancy Feast stove that you punched out in two minutes in your garage.
That said I've personally been slowly moving more toward minimalism, and I'll probably be experimenting with the Fancy Feast and similar stoves this summer.
Now, if in fact your question IS "why do you all like alcohol stoves in general", well, that'll start a flame-war. But in short:
They are light. The CC is actually one of the heavier ones- you can certainly find lighter. In particular they are generally considered lighter than a compressed gas stove for trips of about 5 days or less, considering the fuel usage of the typical UL hiker. There are those who argue that point though, and there are those who claim that they are lighter on longer trips, too. And, clearly not everyone has identical fuel use habits.
They are fun to fiddle with. A normal (i.e. non-engineer, non-machinist) person can make their own and play around with them if they so desire.
They have no moving parts to fail, unlike a compressed-gas stove. Most have no seals to fail, either.
An acceptable fuel is readily available almost anywhere in the world, and not dependent upon finding a hiking store. The canisters (and even the fuel in them) vary around the world. I'm not sure that Esbit would be available in a remote village in Transoxonia, but I'll bet that nearly-pure ethanol or denatured alcohol of some sort is.
The fuel is multi-purpose. It can be used as a hand sanitizer, or improvised medical sterilizer. If it is ethanol it has recreation uses...
I mean, if your ONLY concern is weight then don't bring a stove at all. Live off of snack bars and food that can rehydrate cold.