That isn't quite how it was envisaged to work.
My recollection of the plan was that only peak hour trains would have first class, and, by making the train have one common type of interior, the amount of the train devoted to first class could differ depending the service. On a 12-car train, rather than having an area of first class in each unit, instead one whole coach in the train could be set up as first class.
I think this approach was quickly deemed impractical to set up, as it would have needed staff to set up the antimacassars in the relevant coach before the train could be boarded. Also, after a split it may have seemed, as you say, that one whole coach was first class in a 375/6.
Consequently, a dedicated area was later set up in each unit