I'm just curious what the physical limitation is now-a-days that connectors like USB-C and thunderbolt exist. In the past I thought the issue was that the encodings that video cameras put out (probably mostly some variant of h.264 or h.265) required more throughput than USB could offer but now that doesn't really seem to be the case. What's the issue?
It's theoretically possible, so there is no longer a physical limitation owing to bandwidth as you mentioned. However, it is costly and time consuming for the camera manufacturer.
It would require them to choose from one of a few options for delivering video live and on-demand which would impact quality, cost and user experience. One method is to use the standard USB camera device protocols that webcams typically use. A very different technique would be to encode H264 into an Internet based streaming protocol and send that through USB. Yet another is to use WiFi with a proprietary app which some cameras use. Each have their advantages and disadvantages.
There are products that span all of these options and others that have HDMI or SDI outputs. It seems like output method is more of a question of use case and product specialization than it is a physical limitation anymore.
I am not 100% sure but I think that there is a need for a minimal system managing the Internet Protocol in order to enable streaming. So it means there would be a need for a CPU, an OS, and a interface to setup all the related settings to the camera too.
I think the computing power needed for video compression would be possible thanks to a recent processor like the one embedded in smartphone. And of course the rate is no longer a problem for new connections. USB-C would even be able to stream raw video 4K 60fps = 12Gbps. Which is fine for be DisplayPort 1.2a available on USB-C