Most USB-C devices really only support DisplayPort for video output.
There's an HDMI "alt mode", but almost no device uses that directly; most USB-C-to-HDMI adapters and cables are accordingly really combined USB-C to DisplayPort and DisplayPort to HDMI converters and translate one protocol to the other at the electrical and logical level.
Compared to lighting it only has advantages, faster charging, more universal.
It's only a nightmare because you can carry almost anything over USB C incl. DisplayPort etc. which is not always clear if it's supported or not