Saying women make the endogenous choice to do more housework because the system encourages them to do so is... I suppose an affirmation of the problem? In a roundabout way.
If we are forced to make a self-sacrificing choice because (a) our system conditions us to do so, and (b) caring work needs to be done by SOMEONE, then this is not a choice. It's a grim reality.
We need a new system.
We need the ability to make better "endogenous" choices about how we spend our precious, human, and (in this case) female lives on earth.
We made the system we are in. We have the ability to make a better one. And we should.
Because I would NOT make that choice personally, yet I do because otherwise housework and childcare simply wouldn't get done.