> humanity has some deep desire or curiosity for robots to look like humans.
I don't think you can draw that conclusion. Most people find humanoid robots creepy. I think we have a desire for "Universal Robotics". As awesome as my dishwasher is, it's disappointing that it's nearly useless for any other task. Yeah, it washes my dishes, but it doesn't was my clothes, or put away the dishes. Our desire for a humanoid robot, I think, largely grows out of our desire for having a single machine capable of doing anything.
The vast majority of “universal robots” are portrayed as humanoids in science fiction. Perhaps part of the reason is that true “universality” includes socializing, companionship, human emotions, and of course love.
Or, alternatively, general-purpose robots tend to be human-shaped because the world as it already is has already been fully designed for humans. Single doors are tall because that's the size of a human. Tools are designed to be held in something like a hand, sometimes two of them. Stairs are designed to be walked on, and basically any other traversal method just falls apart.
Of course, there is also the thing where authors and artists tend to draw anything with human intelligence as humans, from robots to aliens. Maybe it's the social reason you mention, or they just unconsciously have assumed humans to be the greatest design to ever exist. But even despite this, in a human world, I expect the first true general-purpose robots to be "standing" upright, with one or several arm-like limbs.