People keep talking about the NHS as if it's a single organisation. In reality it's around 15,000+ different ones ranging from little GP surgeries to mega trusts that run multiple hospitals around a town.
Part of the problems with the NHS is this fragmentation. You can't stop shipping paper copies of things until all organisations have moved into the late 20th century way of working.
Individual areas do collaborate and there are some shared services but it's despite the structure rather than because of it.