As I suspected, you get 4K HDMI at 30hz, which is awful to work with.
The 4K @ 60hz issue is still a big one with these. You have to have a dedicated dongle for it.
The problem is, current USB-C hardware can't support 4k@60Hz and USB 3 speeds over a single cable.
The USB-C cable has 4 high-speed wire pairs (lanes) capable of carrying USB 3.1 data, plus a spare low-speed pair that can carry "legacy" USB 2.0 data.
In DisplayPort mode, either one, two or four of those lanes are
physically allocated to DisplayPort data. For low-res displays or 4k@30Hz, one or two lanes are sufficient, leaving two or three lanes free for USB 3.1. Unfortunately, 4k@60Hz requires all 4 lanes for DisplayPort, which just leaves the spare USB 2.0 wires for other peripherals.
This is because current devices only support DisplayPort 1.2a. DisplayPort 1.3/1.4 supports higher data rates and can drive a 4k@60Hz display with just two lanes, leaving space for USB 3.1 data to share the same cable. Unfortunately, although the USB-C/DisplayPort Alt Mode spec supports DisplayPort 1.3, most of the USB-C controllers currently in use don't, especially the Intel USB-C/TB3 controllers in Macs - bear in mind that Intel's on-chip graphics doesn't do DP1.3 either. Of course, the display would also have to support it...
(AFAIK all USB-C to HDMI adapters use a DisplayPort-to-HDMI converter - there is a native "HDMI alt mode" in the pipeline which takes DisplayPort out of the equation, but I don't think that's currently in play).
Thunderbolt 3 is still limited to DP1.2a (insane!) but rather than
physically allocating some lanes to DP (DP 1.2a actually wastes almost half the bandwidth of each wire pair), it moshes the DP and PCIe data together so that they can co-exist on the same physical wires and not "waste" bandwidth. This is much more efficient and - combined with the fact that TB3 runs the cable twice as fast as USB-C anyway - means it can easily support 4k@60Hz, and even 5k - although 5k actually uses two 'virtual' DisplayPort cables. The downside is that while DisplayPort-over-USB-C
is basically DisplayPort and only needs a simple adapter at the display end, TB3 relies on a full-blown TB3 controller (or dock) at the display end.
See:
https://www.vesa.org/news/vesa-brings-displayport-to-new-usb-type-c-connector/
Still - 4k/5k displays are still bandwidth hogs and if you want to run them alongside a performance-critical high-speed TB3 or USB 3.1 device, I'd strongly advise subjecting yourself to the indignity of plugging
two cables into your computer.