That presupposes that lighting up and drawing pixels is most if the overall power budget. Moreover, the biggest component of screen power usage is the backlight, which doesn't scale linearly with the number of pixels.
See: http://www.displaymate.com/Smartphone_ShootOut_3.htm. At the same brightness level (Anandtech uses 150 or 200 nits I think), the FHD displays use only 15% more power than the iPhone display despite almost 3x the pixels. And total display power is probably about half the power budget.
Read how that test is run. It's showing a static image. There's nothing changing, there is no rendering in that test at all. So of course resolution didn't have an impact, the test is built to test purely the display's power draw and does excactly that.
