I used a tuna-can stove on the AT for 4 months. It worked well & certainly has a place in the lineup of options for bike camping. I would caution anyone considering a home made alcohol stove to experiment at home and on short trips before choosing one for a long trip. The nice thing about biking is that the weight of your load isn't actually riding on your body - its on the bike. Carrying an extra pound of stove isn't as big a deal when bike touring. For those that choose to go ultra-light, its a great option. But its not for everyone.
I can recommend it for those that: like futzing with their gear / making their own stuff; people that are travelling solo (or at least cooking solo); people that are counting grams in pursuit of ultra-light nirvana; people that do not plan to cook at higher altitudes or in cold weather.