That would be really lame but thanks for the heads-up.
Yeah, I was very disappointed with the USB-C controller on one laptop I had from work that didn't support the second monitor.
It could also be that it's just that the motherboad has a single graphics processor. To test that, remove the regular HDMI and try running JUST the USB-3 -> HDMI display. If it runs, it's just because there's only a single GPU on the board.
Another scenario I've seen is where, yes, you can run two displays, but you can only mirror the two screens (make them show identical content), but not actually extend them into two different monitor spaces.
Do you have a manufacturer / model of your PC / laptop? Mine was an HP, and if I recall I ended up calling their tech support, and they told me that.