So my question is why does it need another plate to be the face. Why not the face act as one of the sides?
Sometimes the front-facing drawer side does also serve as the drawer face. There are various joints that can be used to connect the front to the sides while hiding the joinery from the front (e.g. locking rabbet joint, half-blind dovetails). These joints are great if you want the drawer faces to be flush with the front of the cabinet.
They're not so great if you want the drawer faces to overlay the cabinet front, though. You probably could start with a thick piece, cut a rabbet around the edges, and then join the sides of the drawer to the remaining thick part. It's much, much easier, though, to just build the drawer box first, and then attach a separate drawer front. Not only is the joinery easier, but keeping the drawer fronts separate and adding them at the end gives you a lot of room to adjust. If the drawer doesn't fit perfectly in its space — maybe it sits a little too high or low, or a bit to the left — it doesn't matter, because you can position the drawer front correctly on the cabinet front and then attach it to the drawer. If you have a series of drawers, you can adjust the drawer fronts so that they're spaced evenly, and even trim them if needed, without having to modify the drawers.