[vel0city]

There just aren't enough pins. In USB Type-C DP Alternative Mode with 4xDP lanes, you've got 12 pins not including ground and power as it also does USB 2.0 in there. A single-link DVI cable or HDMI takes 19 pins. Regular DP could do it because regular DP had 20 pins to map to things. DP Alt Mode works because its pretty much just directly using the DP signaling on the four lanes and ignoring some of the other optional features of DP.

Any USB-C to HDMI adapter is an active adapter; practically nothing supports the USB-C HDMI alt-mode. That USB-C hub with HDMI is either doing things with a DisplayLink chip or it is doing USB-C DP Alt Mode and then doing an active converter from DP to HDMI. DisplayLink is pretty common on USB docks and can perform decently well for a number of tasks, especially the kind of workloads you'd expect for a Chromebook. And they'll work on pretty much any USB 3.0 (and even sometimes USB 2.0!) ports.

https://en.wikipedia.org/wiki/DisplayLink

Active adapter just means it is performing some kind of signaling modification. Chips can be quite cheap these days.