Webcams are low cost and can produce surprisingly good results however often they are packaged in such a way that makes them less useful in certain applications. If you are working from a laptop as a recording/live encoding device then often USB inputs are the only way to connect a camera to the system without using an adapter such as an Epiphan AVio device https://www.epiphan.com/products/avio-hd/ which significantly adds to the cost.
Being able to swap their fixed lenses for something like widely available low cost CCTV CS mount lenses would be an advantage. Also being able to replace the built in microphone with an external XLR input for improved audio that was always in sync with the video would be an improvement as well.
Perhaps add a LCD preview monitor and 3D print a suitable housing with tripod mount and this would give the potential for a low cost 'follow cam' which would be more manageable yet still be able to plug into a laptop USB port to allow it to be used with a wide range of existing software.
In parallel with this then a similar problem appears to exist with the likes of the PiCam CSI devices. Even though there is potential for relatively high quality capture the camera modules often have fixed lenses which are often not suitable for the task in hand be it follow cams or close-up work. ArduCam Raspberry Pi Camera from ArduCAM appear to provide one potential solution in this area, however perhaps the show could turn something like this into a R-Pi open format IP camera.
Up until now I've been using the AXIS M10xx series of camera as a low cost camera for live streaming of 24/7 type activities however as per the USB webcam dilemma they have fixed lenses which aren't always suitable. Other cameras I've looked at have had other problems such as not supporting WPA-2 Enterprise authentication or have limited control over the image processing options. I know that shabaz has been working on something similar with the HAL-CAM 9001 project HAL-CAM 9001 – Building a New Security Camera however it has the fixed lens issue.