And where if you have a non-computer device, having a HDMI port forces you to not have any other ports due to licensing. Ever wonder why most TVs and Home Theater Receivers do not come with DP ports?
Legacy and network effects: home A/V has HDMI because HDMI is on all home A/V equipment. At this point you can probably have either/both and things would work fine.
One technical distinction for HDMI is perhaps having CEC.
Home theater receivers use HDMI because the vast majority of things a home user is going to use with it also uses HDMI.