I worked as a freelance DOP and worked with cameras + lenses that coat more than a decent car.
And while there is certainly room for improvement with typical webcams: the problem is in many cases not the camera, but the conditions under which it operates. Low light, shooting against the light, smeared laptop lenses, weird angles (not eye level), weird perspective framing, bad combination of light and framerates, mixed light temperatures, low CRI lighting, etc. If you take an 40k€ Arri and a 20k€ Zeiss Prime and do all of the above the result will still look more or less crappy.
Making a good looking image that feels natural is work, and while the camera is an important cog in the machine, it alone won't do wonders. The whole physical space around the motive needs to be arranged the right way, light fixtures that can cost a ton as well are set up, a whole truckload of grip is placed etc.
IMO we will get photorealistic realtime avatars with cinematic lighting before we will get cameras that create better pictures on their own. Or the crappy webcam pictures are filtered in ways that make them look acceptable etc.
Making a good picture involves realising how somebody looks and how they want to be seen and get them closer to that goal, it is not something where one size fits all.