I think the closest practical solution might be a Trail Designs Caldera Keg system, Jetboil, or another system that I'm embarrassed to admit I can't remember the name. The idea is a lightweight stove integrated with a mug.
OK-The Caldera Keg has the windscreen integrated as the pot stand. The 12-10 stove is highly efficient. The system has a couple of silicone bands, one is a pot grab point and the other, a lip guard, as I understand it. Trail Designs also has a "graham cracker stove" that is supposed to optimize the performance of an Esbit tablet.
The Jetboil is one I've seen but not used. Many people swear by theirs. MY take is "too heavy."
If you can find one, there was a stove/stand that held an Esbit stove below a Heineken or other large beer can. After the water was heated in the can, the stove stand could be reconfigured around the beer can pot, then the windscreen went around the can with a little air space. In effect, the stand and windscreen became the outer wall of a somewhat insulated tall mug. I tested this for Backpack Gear Test some years ago. The review seems to have been deleted and I can't remember the name of the system. My test item should be buried somewhere in my gear collection.
If all you want to do is heat water for coffee and drink from your pot/mug, any of the above will work. So will a good alky stove with a pot like and MSR Titan or even a recycled 12 oz Vienna sausage can-pot. Either of these work well enough with fuel tablets. I have used small aluminum cans (sausage or beer) with pads made of high temp RTV silicone spaced for grip points. I could make a sleeve from windshield reflector, if I want more insulation...