Inside a plug there is one grounding wire, while the socket has two grounding pins. I know that the wire splits into two, but why? As the wiring inside the wall is supposed to be the same between different types, I assume it is just a design decision, however does this mean that in such design I could theoretically have one broken pin for grounding and successfully ground a plugged device only by using one pin on the socket?
Figure 1. Schuko sockets. (Image source: Bran.)
If you are referring to these sockets the dual earth pins give balance pressure on the plug which would otherwise be forced to upwards or downwards making insertion difficult and possibly affecting the contact of the L and N pins in their sockets.
... does this mean that in such design I could theoretically have one broken pin for grounding and successfully ground a plugged device only by using one pin on the socket?
Yes, but it is most likely that the two contacts are stamped out of one sheet of metal and there are no joints so fracture or breakage is unlikely.
Your claim is not true. EU socket/plug standard is a combination of
almost all older standards in the EU. It was design that german DIN standard plugs are somewhat compatible with italian or french ones. Czech plugs are also in compliance with. So...
German standard was rotation symmetric meaning the hot wire is on the left in the wall but in the device it could be one or another. For having the ground wire allways connected to the ground means one have to use two ground connections. Plus the two spring-loaded contacts cancells out the net force.
Italian standard, on the other hand, use anther approach to the symmetry - one central ground connector in between hot and neutral. The outer shape is flat hexagonal and is same as "other" european 2-wire 230 VAC connectors.
French standard was hot wire plug on the left, neutral plug on the right and ground pin above them. Meaning no rotation symmetry.
The standards were changed to gain the compatibility. The sockets in Czech Republic, which followed the french standard, are round (no notches) with the groun pin; the plugs are notched body (to fit in german socket) wit both hole for ground pin and notches for the german ground connectors. The universal EU socket would look like this:
You can see there are no notches, so all round, flat or nothed plugs will fit in. Also it accept two different hot-neutral distances (I think old italy was wider than old german/french). There is also the Italian central ground plug and german top-bottom connectors. This socket can accept any old and new european socket. Except for UK, because,... You know, UK. And old french/czech plugs will lose the ground connection because they do not have the notch. A design failure, I may say...
In the UK we have a single earth pin. The 240V single phase is between live and neutral the latter bonded to earth at the supply. Properties typically run off one of the three phases of the 440v supply in blocks of 6 or so. Utterly different from the us model.shuco plugs are an abomination! The 13A plug with its shrouded sockets and live snd neutral pins making contact after earth (and with insulated shanks) are remarkably safe.