OK, but network rail don't have any in-house building skills. Actually they don't even do much truly in-house maintenance/fix work - it's mostly contracted out.
Network rail are not building east-west rail, let alone HS2.
True, but that is why I am sceptical about benefits of re-nationalisation. The skills are not going to come back.
The default assumption these days is that everything will be contracted out. It needs a cultural change and a lot of investment to change things.
The train operating companies are mostly privately owned but they do not build the infrastructure. Quite a few are state owned though (LNER, Thameslink, Scotrail, Northern...)