Upgrading 1.4 HDMI port to a 2.0 HDMI port?
At CES, HDMI 2.0 TVs were demonstrated as well as 8K displays. I do not think the current HDMI port provided by Apple will be sufficient.
Don't stare yourself blind on HDMI 2.0 since the HDMI-signal is on the same bus as the Thunderbold 2 signal which already supports 4K 60fps.
Second, electrically, HDMI 2.0 is exactly the same so a firmware update should be enough.
Don't forget that HDMI is originally designed for DRM. So in the end you are better off buying an adapter (TB to HDMI or DVI which is the same without audio) and use an optical Toslink cable for audio which gives the ultimate quality since it is optical.
So, to conclude that the Mac Pro 2013 is obsolete due to a connector-type is rather silly to put it mildly !