What I could see happening is, however, USB-C shaped Displayport 1.3 ports that could carry 2 4Kx60Hz signals. This would be similar to how the current MacBook has USB-C ports for display info, but no thunderbolt support.
Exactly this. Probably some combination of a full size HDMI 2.0, a full size or mini DP 1.3, and one or two USB-C ports capable of sending DP 1.3.
It's unlikely that AMD or NVIDIA would include a Thunderbolt 3 port on their next gen cards, since TB uses DP to send video. Currently, TB3 only supports DP 1.2, which makes it inferior to both DP 1.3 or to USB-C (which supports DP 1.3) for video purposes.
It's ultimately Intel's call to update Thunderbolt for DP 1.3, and as such AMD and NVIDIA will probably avoid it.