Higher resolution monitors do not necessarily draw much more power! Most of the energy goes into the backlight, which is largely constant irrespective of the resolution of the LCD panel in front. Similarly with OLED, the power consumed is mostly a function of the total lumens the panel puts out, not the size of the individual pixels.

You'd need more powerful video cards, sure, but for typical 2D graphics, the difference is on the order of 5-10W, which isn't exactly going to boil the oceans...