Maybe people have a different setup that I, but I usually remain the same distance away from my monitor at most times.
I'm guessing you mean "shallow depth of field" rather than "sharp" here.
And you probably don't want it to be so shallow so a few centimeters would matter, then your nose could be in focus but your ears not, or vice-versa. That's a bit too shallow.
It also doesn't require auto-focus, it requires you to be able to put the camera at a good distance with the correct f-stop, or being able to change the f-stop one way or another.
Auto-focus is more for cases when the subject/object moves a lot forward/backward from the perspective of the camera, so you don't have to manually adjust things.
I doubt a small sensor auto-focus camera will achieve that though.
Webcams in poor lighting conditions benefit from autofocus, because autofocus makes it easier to use a larger aperture, improving low light performance.
Laptop webcams benefit from autofocus because there's no room for manual focus controls, and the distance to the user will vary substantially depending on if the laptop's in a docking station, if the user's leaning in to read some small text, etc.
Meeting room webcams benefit from autofocus so you don't need a technician to attend every time it gets knocked out of focus.
PC webcams sometimes benefit from autofocus, because the cable usually weighs more than the camera, meaning the camera often gets moved and knocked about. Plus about 95% of home users with manual focus webcams don't even know they need to focus them.
Streamers have great lighting and cameras firmly mounted on solid tripods - but they're often using mirrorless interchangeable-lens cameras, so they get autofocus for free anyway.