It's been forever since I read the play so I looked it up. Leading up to that, Cordelia thinks to herself in an aside that basically she doesn't know how to put into words her feelings, especially in a way that sounds genuine given the expressive/over-the-top speeches by her sisters.
I see your point with her response, but I think it's somewhat more complex than just saying "I love you according to my duty":
Good my lord,/
You have begot me, bred me, loved me: I/
Return those duties back as are right fit,/
Obey you, love you, and most honour you./
Why have my sisters husbands, if they say/
They love you all? Haply, when I shall wed,/
That lord whose hand must take my plight shall carry/
Half my love with him, half my care and duty:/
Sure, I shall never marry like my sisters,/
To love my father all./
The ending part is somewhat sarcastic in terms of calling attention to her sister's insincerity, but it's kind of like a meditation of filial/familial love in the context of different social roles, and I think the idea is that they don't allow one to express the depths of affection. Because the first line is basically saying that "you were a loving father to me in all that entails and so I'm a loving daughter to you in all that entails".
It also does strike me that the fairy tale derivation, which has a happy ending, involves the Cordelia equivalent saying that she loves the father "like meat loves salt" (or something to that effect) and later illustrating it by serving unsalted meat to him. So, I think in both the fairy tale and the play, there's an underlying understanding that because the contest is a stupid idea, Cordelia/her equivalent gives a sincere but seemingly flippant/sarcastic response.
edited 12th Oct '17 10:44:29 AM by Hodor2