"That is true, I stand corrected, but. The rate of heat loss due to vaporization is miniscule compared to the amount being produced within the cone. Agree?"
No. Water picks up heat at ~100cal/gram. Water->steam takes ~500cal/gram.
Actually a phase change water->steam consumes MORE heat than simply heating the water by about 5 times.
"Before the boil, heat from within the cone is transferred through the wall of the pot at a fast rate. Once the boil occurs, the transfer rate decreases dramatically."
Nope. Heat transfer rates are pretty much governed by the material type and thickness. The difference between 99C and 100C is ~100cal/gram as above. Add in the difference for the pot and you are done. It becomes a steady state system boiling water. It does NOT get hotter than the inside water, (well, not quite true maybe by a couple degrees due to the insulating effect of the metal. But the difference would stay the same same, pretty much, through out the boil cycle. At the low temps you are talking about, ie boiling water, it tends to stay the same.) Open metal is another story, it will conduct heat and accumulate if there is no water, but steam will cool it. Soo, it will have a higher heat. But not that high. Example: like soldering a pipe with water in it, you cannot do it. Though you might slab solder over it.
"The area within the cone becomes an oven that keeps getting hotter and hotter."
Well, maybe. There are other avenues for heat to disburse. IR is one. Vents are another. If you don't have enough vents, then the flame is limited by flue gasses. Not enough oxygen to burn. It will usually just form a new steady state system, not continue to accumulate heat.
"Keep in mind that the stove is not touching the bottom of the pot in the case of the 12-10 there is no possible way for the stove to maintain the same temperature as the pot which is 212 degrees No heat is being drawn away from the stove. It's heating up inside the oven. The flames of the stove are still producing an enormous amount of heat in close proximity of the stove."
No. Infra red radiation is disbursed. Alcohol boils cooler than water, even inside a stove. You are right, the stove will NOT be at the same temp as the pot. Once a burn has gone on for a couple minutes, it should NOT heat up till the very end, as fuel is mostly gone. The radiant energy (IR energy) IS feeding back and the flame IS still producing heat. It can over heat at this point. But, this is a few seconds at most. The fuel, alcohol is assumed, boils off, exactly like water boils off in a pot. It maintains a steady temp. The last bit will "flash" off still burning, leaving bare metel, then go out. If damage occurs to the 12-10, this is when it will happen. It can anneal the edges of the stove, I have several where this has occured. But it doesn't hurt anything, really. It works fine for over 1000 burns. It is fairly well designed, as good as any alcohol stove. If this worries you, you can add a bit of water, it will cool the flame a bit. With enough water, it will stay in the bottom of the stove, keeping it cool. Not really necessary, though.
As far as the OPs question, many stoves will overheat in the cones. Penny stoves, and cat stoves do not work well. Brasslite makes one that does work, but it is too tall. I made up a couple other verions that work well under a cone.
The pleated stove or Apalo or something like that, can be cheated for length to give the output needed. This was a couple years go, as I remember. I made the stoves a couple years before that.
Many alcohol stoves don't work under a cone, not enough air inlets, not enough exhaust. too much heat, too little heat. built in pot stand or something. Chimney stoves work about the best.