It's cheaper to implement than HDMI. So if DisplayPort ports are common on displays, devices will start using it (cheapo devices first). If DisplayPort ports are common on devices, displays won't need HDMI anymore. Plus, industry-wide, it's wildly inefficient to have one high-bandwidth video connector for monitors and a different one for TV's when the technical distinction between those is pretty much non-existent and we could scale our engineering effort across a much wider set of devices.

So, after a transition period, cost-saving will eventually lead to DisplayPort taking over.