My feeling is that he does things for her only when he wants something from her (or when he's pulling his misguided chivalry/overprotective schtick)

And in our case, forcing Elizabeth to be the stay-at-home mom is exactly the overprotective thing to do. Just like in the finale, I can see them arguing over who's going to do X or Y, and then Philip slips out the back and leaves Elizabeth with the children.