Why doesn't a wing in supersonic flow produce a shock that results in flow parallel to the leading edge? When we look at a wedge in supersonic flow, a shock emanates from the leading edge such that the flow after the shock is turned and is parallel to the airfoil surface.

The shock angle is based on the flow turning angle (wedge angle) and can be found using the chart below:

I was wondering why a wing in supersonic flow would not have the same behavior (see image below). That is, why wouldn't there be a shock emanating from the apex of the wing (which depends on the sweep angle much like the wedge angle ($ \theta $)? If this were to occur, there would be no component of the flow perpendicular to the wing (as the shock would turn the flow parallel to the surface). I know this doesn't occur physically because there is always a component of flow perpendicular to the wing, but this confused me because the wing seems exactly like a wedge (if we look at a wedge from the top instead of the side).
Air needs to make way for the approaching airplane. For that, it takes the route of least resistance, which is above and below the wing. This is shown in your first picture which is valid for a supersonic leading edge. Your top view shows a different cross section through a three-dimensional shock at a much lower speed. The vector M$_2$ is wrong and does not correspond to what is really happening.
If X is in flow direction, Y is sideways and Z is down, picture 1 shows a cut in the X-Z plane for a supersonic leading edge. Picture 3 shows a cut in the X-Y plane for a subsonic leading edge. Here, air does not flow sideways but continues past the shock along the direction of the vector M$_1$.