I'd have to rearrange the room to accomplish that, there is nowhere close to enough space behind my monitor to put a tripod. It would also block all the LED lights I have on the wall (I'm a bit obsessive on this subject), necessitating more changes. The wires also rapidly become annoying, since unlike a monitor-top webcam they can't be bundled up with the HDMI/Power for the monitor.
The further back the camera gets too, the less "real" it feels to your audience. Humans can tell where each others' eyes are focused, and the further the camera gets from the plane of where your eyes are focused (the monitor), the more it will feel like that you're not paying attention to them. This means the ideal place to put the camera is right on top of the monitor, exactly where we put webcams today. This might be doable with some cameras, but certainly mine is too heavy to pull this off. Perhaps a boom arm system would do the trick, at the minor cost of making my sit/stand desk less usable.
If you're going to try and use a real camera to improve video quality, I think you really need to go whole-hog and build a teleprompter setup. That's the right way to make it possible to see something and have your eyes focused on the right place without having to dodge around getting a monitor to work correctly. This is completely doable, albeit a bit excessive, but probably well beyond what's worth it for anyone but the most obsessive or those whose jobs involve being on camera a lot. Maybe if I was CTO it would be worth it just for extremely high-fidelity all-hands, but that's not my current situation.
My top tip is to use a full-size dining room table as your desk, rather than something sold as a modern desk. Then your monitor sits about in the middle of the table and you have so much space behind it, around the sides, and beside you. It's a huge improvement to have this extra space.
Things marketed as 'computer desks' are invariably about 4x too small for comfortable use and placing your equipment on.
You can make it work, if you rearrange your entire office space around this requirement. I personally wouldn't recommend it, but to each their own.