Thunderbolt is much more than an just a display link. You can think of it as something as PCI Express, plus some USB and displayport compatibility. It can technically support everything, but might require custom drivers. I don't expect it to become a mainstream solution for "just pushing down some pixels from A to B" due to its additional complexity and cost.

I haven't followed USB4 too much. I expect it to again have multiple "levels" like USB had before. And whether some or all of those will be high definition video capable it to be seen. For USB-C video was just a mere alternate mode which switched the meaning of the wires inside the cables to displayport. Doing video over the PCI Express subsystem of thunderbolt is a different story.