I think it would be possible now.

Bluetooth keyboard and mouse, of course, already on the desk. Chromecast hooked up to the monitor. Use one of the Android automation apps to automatically mirror the display via Chromecast when the phone is in range of the BT keyboard / mouse on your desk and when it is laying flat on a surface (plopped onto the desk).

Not perfect. Chromecast latency might be an issue. You would still have to plug it into a charger if you don't have wireless charging. But it should work.