I think Arthur's answer provides a good framing for this - nobody "should" have to do any house work, it's just a "necessary" evil in today's time, so there's no objectively right or wrong answer.

That being said, I think it may or may not be the most fair way of doing it depending on whether the house work is roughly the same amount of work as the job or not. I guess chances are it isn't, but it may be more or less. If it's more, then the person with the job "should" do some of the house work. But there are other extenuating factors, like what if the stay-at-home person is disabled? Or what if menial labor makes them more miserable than it does the person with the job? Or what if the house work is somehow harder than the job? Etc.

But anyway, again, what's best is ultimately just whatever the couple agrees to...