'Kuwayaki' has a similar origin as 'sukiyaki'. 'Sukiyaki' might just remind you of the song but it is also the name for Japanese popular meal which we associate with westernisation or special occasions. The both 'kuwayaki' and 'sukiyaki' cooking methods used to require agricultural implements: kuwa and suki.
I heard from my father that before opening of our country we didn't eat meat (with a few exceptions such as rabbit, birds) because of Buddhism philosophy. But if a cow who used to help agriculture dies, farmers would eat it. But as they couldn't use the same pan or pots they cook for other meals, these are things farmers would find still usefull for cooking. Of course now we don't use such tools but it is quite interesting to know how we tried to appreciate things that were available to us without feeling guilty of wasting things and ruining discipline.