You would think...but that doesn't seem to be the case.
For instance, I have yet to see an HDTV that takes a real 120 Hz video signal from a computer, while a monitor most likely will over DVI-D or DisplayPort. HDMI doesn't seem to have the bandwidth for 1920x1080 at 120 Hz, let alone 2560x1600 at 60 Hz.
DVI will disappear one day...but that's because DisplayPort is its replacement, not HDMI. I'm pretty sure I recall hearing about how DisplayPort 1.2 will have enough bandwidth for 4K resolutions.
That still doesn't resolve the audio path issue, though. DisplayPort is still video-only...and HDMI is still held back by the consumer electronics industry's lagging standards compared to the computer industry's bleeding-edge offerings. The ideal solution would be to just use HDMI strictly for audio output, but I'm not sure if his current equipment would allow that.