The stoves themselves are very light, the fuel can be bought at just about any hardware store, alcohol is a renewable resource which keeps the hippies happy, they have no (essential*) moving parts, and there is VERY little residue/smell. They are also easy to build with a soda can**, which fuels a lot of "look at what I built" posts & videos.
The downsides are that the stoves just aren't as hot as pressurized fuel stoves, alcohol burns with a "clear" flame in daylight which is a bit of a safety concern, and the energy density of alcohol is lower than fossil fuels.
I'm on the fence. For shorter trips in warmer weather alcohol makes sense. Although alcohol will almost always light, I get tired of waiting for it to heat water in the cold. If you need more than a few days-worth of fuel, or are cooking for more than 2 people what you save in the stove gets offset by the worse energy density of alcohols compared to isobutane or fossil fuel.
* Some commercial alcohol stoves have a little damper-paddle-thingy to control the flame. If it gets lost the stove still works.
**Soda can stoves are prone to getting squashed if you pack them wrong, so be careful there.