Q: Do the old Japanese values of "Men work and women stay at home" still exist?
Answer: Yes, there are still some. I think that tendency is particularly strong among SMEs.
A Japanese worker would be puzzled to hear that a non-Japanese male worker, even though a dedicated employee, refuses to travel when his wife is due to give birth, for example. Traditionally in Japan, the husband’s job is to work outside the home, and the wife is responsible for everything in the home. Things are slowly changing because more married women work outside the home, but this division of work is still overwhelmingly the case for men who work for global companies. The husband gives his paycheck to his wife, who manages the household finances. She even determines the amount of pocket money he receives each month. She takes care of the children, the shopping and cooking, and household cleaning and repairs. She would no more ask her husband to help her with the housework than he would ask her to help him with his job.
When it is time to give birth, the wife handles things herself, or ideally, returns to her mother’s home to be looked after. Giving birth is the wife’s job. The husband’s job is to do what the company requires of him, including any and all travel.
Most Japanese wives would never consider calling their husband’s at work, not unless someone had died.