Well, I gotta tell you: I think this list is a pretty solid answer, for us, to the problem of housework. I am not necessarily claiming it is an answer to the problem of childcare.
We had been using some variant of this list for four or five years before we had children. We basically kept right on using it.
The labor of childcare has two parts. One part is simply increased housework which is similar to other housework: kids throw mush on the floor, they draw on the walls, they go through five pairs of pants in a day.
But another part is not really reduceable to housework. Bathing the kid? Singing "the itsy bitsy spider" while diapering? Reading a book together? Having a debate about gay marriage (a perennial debate topic for Aviva and me)? It's a slippery slope, because some of these activities look like housework, sort of, but others don't, but they're all kind of the same thing, so where do you draw the line?
We essentially excluded all varieties of "giving love to children", from bathing them to singing to them to oohing and ahhing over their artwork, from the whole equation. For one thing, we felt icky rewarding ourselves with points for giving love. For another, while we would fight about who had to do the housework, we would fight about who got to be with the kids. We figured there was enough intrinsic incentive to do that, less onerous, part of childcare.
If any particular category becomes a particular pain in the ass, you can always say "let's start putting that on the list". Say you had initially categorized arranging babysitters and playdates under "taking care of the kids", but then you realize that it's actually just scutwork, and not about quality time at all -- then you can make it a chore item, if you can find an appropriate granularity ("organized 5 playdates").
Now, it is undeniable that this is a place that sexism can creep back in, and surely has, despite our best efforts. If one parent is out playing sports and the other is home with the kids, well, the one who's home is probably doing housework and thus getting ahead on the list and thus earning more time out... but arguably not at the optimally fair rate, if they spend a lot of that time reading bedtime stories and intervening in disputes instead of things that "count" on the list.
But nor would it be fair the other way -- I can tell you right now that if childcare counted on the list as chores, it would destroy the usefulness of the list for us.
The way it is now, if the kids and I spend my stay-at-home-daddy days one week building homemade telegraphs, watching The Wiz on youtube, and making up songs, then I get way behind on The List, and the next week I am all about organizing the kids into cleaning squads. But if I got points for the romping? The household maintenance would go to hell.
So instead of corrupting our housework equity system, we end up adjusting non-housework-related unfairness at a much more crude granularity ("I've been doing the brunt of evening childcare, so from now on Wednesdays are my night off").
It's not as elegant, but it works reasonably well. Having the housework, at least, be fair is, to be frank, most of the battle. Childcare is, I think Esther would agree, mostly its own reward.