The TL;DR is that the organization that controls the HDMI standard won’t allow any open source implementation of HDMI 2.1.
So the hardware is fully capable of it, but they’ll get in trouble if them officially implement it.
Instead it’s officially HDMI 2 (which maxes out at 4k @ 60Hz), but through a technique called chroma sub-sampling they’ve been able to raise that up to 4k @ 120Hz.
However there are some minor reductions in picture quality because of this, and the whole thing would be much easier if the HDMI forum would be more consumer friendly.
In the meantime, the Steam Machine also has display port as a completely issue free display option.
USB-C probably cannot replace either, because the unmating force is too light. A typical HDMI or DisplayPort cable is much thicker, longer and hence heavier than a typical USB-C cable (even those specced to carry high bandwidth, like a thunderbolt cable) because they need better shielding to carry high bandwidth signals long distances - it’s not unusual to need to route HDMI several metres (but USB-C cables that long are unusual because of the different purposes)
For TVs and such it’s useful to have the inputs connect vertically, so that they don’t stick out the back of the device and cause problems pushing it against a wall. Then the weight of the end of the cable is going to be trying to pull the connector out of the TV. DisplayPort connectors can have a latch to deal with this.
Of course, there a ways around this: a new connector, for example. But it does mean that you can’t just leverage the existing pool of USB-C connectors and cables to make this ubiquitous.