As someone who works for Airbus...
Airbus now is the conglomeration of many old companies - as recently as 2014 there was a merger bringing in EADS Astrium satellites, Paradigm security, Eurocopter, Safran launcher services etc. into Airbus GROUP. Not all of these are related to the building of planes, but they all had their distinct fields of work prior to being merged.
Specialisations for designing certain parts of a plane/spacecraft are kept locally. The team specialised in optimising engine performance doesn't need to know about the avionics system, the team in charge of landing gear doesn't give a Gnats knee what the windshield looks like.
What determines the specialisation where, in this case, is in some ways related to the previous specialism of the absorbed company/site. I don't know a great deal about the Airbus aircrafts business history, so I'll digress from planes into an area i'm more familiar with.
Airbus Portsmouth used to be an EADS Astrium site, before that it was Matra Marconi, before that Marconi Electronic Systems... who produced electronic components for space purposes.
Nowadays, in PTH we make payloads for satellites that get fitted to the "bus" built in Stevenage, that gets coupled to the transfer module, solar arrays, antennas in Toulouse, and finally shipped to launch from a few places around the globe. This was the case when we were Astrium, and stays the case now.
You've also got to think about the sheer size of the things. You need a vast amount of space to put a wing together and test it - it's just not feasible to move all the infrastructure, and people, to a single location. You'd need to build a small town around it to accommodate all the employees - And then convince them all to up sticks and move to the new site.
In terms of manufacturing wing-size things in one place and transporting them to another country.... I give you the Beluga, Specifically modified to do exactly that.