Why isn't there just one pin (like in French type E)?
Figure 1. Schuko Type F socket. Source: International Config.
From a mechanical point of view the double earth contact in the socket balances the forces applied during insertion and removal. Without it the one spring would push the plastic plug against the plastic socket on the other side.
Most electrical socket connectors pinch the pins. This arrangement does the same thing - just with a very wide socket.
It doesn't. It has two side contacts that make the ground connection.
It is designed to be inserted either of two ways. Since the ground connection is not on the axis of symmetry, there must be two of them.
In contrast, the type E can only be inserted one way to begin with, because it is not symmetric.