But where has the OP said that he gets more downtime? She's listed things like his Costa coffee on the commute as 'downtime' , and listed eating and sleeping, but nowhere has she said that he actually, I don't know, sits around watching TV while she can't.
You're also overthinking the delegation comment , it's not as corporate as a 'managerial position' or something extremely complex. Obviously as the SAHM it's clear that she's responsible for the bulk of the housework. So if she wants something doing, she should say so.
In my house for example, we have our areas, for example he does laundry +pet stuff and I cook + wash up. Jointly agreed. I won't do the laundry unless he asks me to, because that's his job. Similarly he puts his dishes in the dishwasher but he won't wash up pots and pans because well that's mine.
The 'see it sort it' method works for things like water spilling or glass breaking of course the first person has to clean it up! But for everything else, it makes no sense.
It implies that the first person to see something like a full laundry basket should put a wash on. But depending on our schedules, on any given day one person is more free than the other... So they'd end up doing all the housework simply because they notice more things. That's not fair.
We know what we need to do and we stick to it. Other stuff that needs doing we write down and just tick them off to allocate 50/50.
The husband sees his own washing and childcare (what's the OP doing while he does that) as his department, what else should he be doing? What routine should be established here?