I feel like this is not so much 'emotional labor' as the 'mental load' of running the house. To me it's useful to keep these concepts distinct. This is why studies show that couples who divide household work by task, rather than alternate, have a more equal division of labor between partners. It's not just the nature of the work (and like... Cleaning isn't emotional labor?), it's also that this situation makes one partner the task manager.

This is why I think 'just do it' is bad advice. The wife still has to check what is or isn't done. My opinion is that couples who are serious about sharing the load should take the time to sit down, list the recurring household tasks (and the time they take), and then divide them as seems fair (and decide if there are any they want to alternate on - eg cooking and dishes might change, but one person never does both). Then everyone knows what they should be doing - and the husband understands why his wife seems so busy!