I can't find a definitive link but there are a few reasons, a lot of which were already covered in the comments.
One, the style in your picture makes the whole place easier to clean. You can hose down the floors in one go and there's no fewer joins between the walls and the floors for gunk to build up. (EDIT: in your picture you can see that the toilets don't even join the floor -- so for that setup I'm pretty sure it's for ease of cleaning).
Two, it's so that people can see what you're doing in there. It discourages drug taking or people having sex in the cubicles because it's obvious what's going on. Also if someone passes out on the toilet (for whatever reason) it's easier for people to notice -- in a fully obscured stall someone could lie in there for a long time. It may also just discourage people for sitting in there for longer than necessary.
Lastly, it's cheaper and easier. Divisions like that can be deployed in any room regardless of the flatness of the floor, or the height of the room, etc. Building divisions that actually fit floor to ceiling might require custom cutting and fitting, that might happen in a big building with dozens of identical toilets but for the odd public toilet cheap and easy is the way people will go.
To add to choster's comment, it does tend to vary widely across the US. I've seen toilets with even less privacy than that picture -- like a door that's you can see over when you stand up. The concerns about misusing the toilets tend to trump the privacy, particularly in public places. But you're right, in many private places they will be more sealed. And there're many places in the world where you'll be lucky to find a door at all -- or many people that care that there's no door there.