HDMI and DP output work fine off this specific port and fit snugly as if they're both intended for it.
It seems to me that the real unicorn is the connector, itself.
As for the video signal, DisplayPort Dual-Mode (DP++) specifies a port that can switch signalling between DisplayPort and HDMI. It seems most cheap DP -> HDMI adapters are nothing but wires, with no active components. However, they would only work on such Dual-Mode ports, which Wikipedia says is actually the norm (even for ports without the logo).
en.wikipedia.org
Considering the modern status quo of GPUs with 3:1 DP: HDMI and monitors that (for some reason) are often the opposite configuration, more motherboards and GPUs could benefit from adopting this combined connector.
I don't deal with a lot of gaming boards, but on the mini-PCs and commodity boards I've seen, HDMI seems more prevalent.
It does bug me that gaming monitors seem more biased towards HDMI, especially since VRR support on HDMI was lacking for so long. However, I guess the mix of ports is probably with an eye towards gamers maybe wanting to plug in their consoles, which are HDMI-only.