I think it is just the case women/girls do cooking/chores in most parts of the world.
The following may partially answer the question, even if not directly.
- There is a saying "Men should not enter the kitchen", which seems to be originally by a Chinese philosopher Mencius. In Japan, this was understood as "Men should not bother such trivial things as cooking".
- In the post war Japan, generally speaking, there was a complete division of labor: Men go to work until late and women do all the housework.
- It is still the case that Japanese workers tend to work extra hours, and have no time for household jobs.
Because of these, there are some truths that girls are left to do the chores. But in reality of course, fathers would do the job if the child is young. Today I guess most single fathers do the household job regardless of children's age. And there are some cooking mangas about such fathers (e.g., this).
At the same time, there is a social problem around young carers. Poor families have no choice but to make children do the things parents (or other adults) are supposed to do.