Yair . . . I think you folks are missing the point and one of the original the applications. Aga's and Raeburn's and other slow combustion stoves have little in common with other cooking systems.
They can be configured to run on liquid or solid fuel. All the ones I knew burned wood and were very economical to run. They used about a third the amount of fuel of the ordinary cast iron stove they replaced . . . an important consideration when all the wood was cut by axe.
The various hot-plates and ovens could run at different temperatures according to flue and damper settings and the big advantage in Australia on outback Stations the rest of the stove stayed relatively cool.
Anyone who has cooked for twenty workers on a conventional double oven woodburner in forty five degrees Celsius will know exactly what I mean. Although a status symbol now "back then" they were a life changing revelation.
Because the stove never went out there was always an abundance of hot water from the integrated system. If heat was needed this was tapped into for room heating with (on the examples I knew) a very simple and effective pumpless thermosiphon tank and radiators.