A person's cooking pot needs to work for him or her, so there is no "right size." For many years I carried a 12 oz Vienna sausage can for a pot. (Goya brand has that size.) I heated (not boiled) about 10 oz of water to just below simmering for one hot meal per day, using about a half of an Esbit tablet. There was enough burn left to heat more water to just above tepid if I wanted a cup of tea with dinner. Most of my hot meals are pre-cooked and dehydrated, so they just need some hot water to soak and warm up. If they are started with nearly simmering water, I can add some more cold water to finish rehydrating, if needed. Boiling water ends up with food so hot that I have to wait for it to cool down anyway. While the food starts to rehydrate, a second cup of water can start warming for tea.

Coffee? "Mountain latte" shakes or some chocolate with coffee beans worked well enough for me. If I have a hot cup of Joe, I end up taking too long to pack up and leave. Maybe I enjoy sipping too much...

Not having winter camped for quite a few years, my routine may well change to more hot meals and hot beverages if I get back into that. I also recently acquired a wood-burning stove which should perform better with a larger pot. The small 10 oz pot is more efficient, albeit slow, used with a small flame, so the half-Esbit is a good option for it.

As to the BSA policy on stoves-liquid fuels carry more risk and have had special rules since my adult children were young Scouts, if not before that. I think the reason alcohol stoves are frowned upon is more of a safety thing. Most are home made, so not covered by any manufacturer's liability insurance. Scouting is risk-averse, especially since they are self-insured. (Or were when we were active.) Is the cook kit for your son to use when he is out with his Troop? Don't they cook in patrols when out together? For that he should need to use group gear and larger pots, right?