Haha, I'm on your partner's side. He is right, we must carefully wash it and it's not easy. But I must say most of the Tamagoyaki pans in Japan are coated. I think some expensive one like copper Tamagoyaki pan might have no coating but it's not common.
I practiced making Tamagoyaki in a regular pan in Germany ... It's not easy to find Tamagoyaki pan for affordable price in Germany 😉 That's foreigner life.