>>700
pouring the heated water from one pot to another allows it to cool slightly, to accomodate green tea better. There's some intense procedure where you pour it into the pot, then into some cups, then back or something, and then as a rule of thumb it should be at a good temp for the tea leaves to steep without burning them, plus it heats the tea cups themselves. Additionally, unglazed teapots were used for a single type of tea as the tea would seep into the unglazed surface and retain the flavour. i imagine if you boiled water in there it might mess with that. this is all rendered obsolete because we have thermometers now.
generally speaking, putting clay or ceramic etc on a stovetop is a pretty dumb idea anyway. it'll just get burned. Use a kettle or a boiler that can be set to specific temperature that is ideal for the tea you are brewing, and pour that into the teapot.
another point, i guess generally its separate because you might wanna make a different kind of tea and dont want to have to boil water twice? oh yeah, and if you heat the teapot itself it's very difficult to control the temperature well because the pot itself will be scalding hot. you definitely cant take that along on a tray for serving.