Sorry, but you got it backwards. Exactly because pixels are /not/ point samples, but have an area, point sampling does not work, and you need anti-aliasing. In

Sorry, but you got it backwards. Exactly because pixels are /not/ point samples, but have an area, point sampling does not work, and you need anti-aliasing. In the limit of infinite resolution/area of the pixels gets infinitely small, point-sampling would be enough. You say it yourself: Since solving the integration over the pixel area is generally hard, we approximate the integration with multiple point samples.