The stove (or campfire) you use should depend on the conditions where you are.
As Aimless pointed out, there are often altitude restrictions on fires--wood sources grow very slowly at high altitude, and those dead sticks are needed to rot and add nourishment to the very thin soils up there. In addition, it's pretty hard to find firewood in popular areas.
Out here in the west, in particular, we have a long summer dry season. often with high forest fire danger, which corresponds to backpacking season. There are often restrictions on what you can use to cook. Alcohol stoves have caused enough fires (due to careless users) that they are often banned in the dry (fire) season. More and more jurisdictions require a UL rated stove with an on-off switch, which means you are stuck with isobutane canister or liquid gas stoves.
I just read that the Los Angeles National Forest has now banned stoves--or any fire source--altogether, which means that "no-cook" is now the only option there. I can't blame them, not after seeing the results of last fall's firestorms in Sonoma and Napa counties (my daughter and son-in-law gave me the full fire tour over Christmas!). It's enough to make everyone extra paranoid, even though those particular fires had nothing to do with backpackers.
The eastern US is subject to dry spells with high fire danger, too, although fortunately not as regularly as on the west coast. During those times, you want to be extra careful, too--good time to experiment with the various no-cook options, ranging from living on Power Bars (ugh) to rehydrating freeze-dried with cold water.
May your trails be crooked, winding, lonesome, dangerous, leading to the most amazing view--E. Abbey