I don't think it makes that much difference which way you look at it. From my point of view, each unit at the centre has their own airspace requirements, systems, etc. LTC and LAC watches are aligned at the centre but still seperate units (I think).
However, Swanwick as a 'centre' has a single safety team for example, covering all units at the centre (LTC, LAC & Ops engineering). It just depends on where you want to make the cut.
The point I was trying to make (badly) is that we should not be referring to Swanwick as LACC, as it isn't any more, and neither is it NERC(
) or LATCC (unless you are talking about Mil)