And the best part is that you don't even need a connector, you can just build it right into your PCB! USB-A also lets you do a PCB-only connector, but if you're doing anything that requires a cable instead of just plugging directly into a port, it's a lot more annoying to require a USB-A extension cable than any USB-C cable.
Do you have an example for such a "USB-C edge connector"? Intuitively I would have said that common PCB thickness is too large, or do I misunderstand what you mean?
Yeah, you need a 0.8mm thick PCB, but everyone can do that now (JLCPCB and oshpark both do it for the same price as a regular 1.6mm board). Here's a footprint: https://github.com/jmgao/PCB-USB-C
Annoyingly, the USB-C midplate is specified at 0.7mm. In my experience, 0.6mm boards are too thin to make a reliable connection. Going thicker has worked perfectly with all of the cables I've tried. I suppose there might be some risk of damaging your cables, but it doesn't seem too likely to me (the spec is 0.7 +/- 0.05), and I haven't had any problems.