But what about vapour barriers, you may ask, that plastic sheeting that everyone installs between the drywall and the insulation? Isn't that doing the same job?

A vapor barrier is not an air barrier
Air barriers and vapor barriers have two distinct purposes. The purpose of a vapor barrier is to prevent vapor diffusion. The problem is that vapor barriers, as installed by most builders, do not enclose the entire envelope and are often punctured either by accident or while installing other infrastructure in the home. That doesn't negate their value, however. A vapor barrier does not have to be continuous to do its job; a puncture simply means more vapor diffusion in that area.