One reason would be to bore a hole to a larger diameter to fit the shoulder of a new pinion. Also can be used to repair a distorted hole or drilling a hole into a disk or into a piece of round stock that is too short to grab in a normal collet. Can be used for facing a small round part. Yes you can hold a gear by closing around the teeth with the proper sized wheel chuck. The fit between gear and chuck must be nearly perfect. If the wrong size chuck is used then damage to the gear teeth is possible. Sets of 10 chucks are common for watch repair as this range will accommodate most watch gears. In my opinion cement chucks are a safer way to go but will take longer to set up and center.
Hope this helps James1983,
Bob