If anything I shouldn't be doing chores, I should be relaxing. Doing chores is working.

As in, I'm being paid to work, some of the process of working is recharge time. By instead doing chores, I'm arguably not recharging as effectively.

Of course it's a bit more complex than that, and uncompleted domestic tasks create mental overhead that distract from focus, so where the balance lies is hard to say.

I do, as it happens, ask for more work when necessary. I like to have a queue of tasks to work through, then take them on at a sustainable pace. So far it's been several years and no one has expressed anything negative about my pace of work. In fact it got me promoted a couple of weeks ago.