BOAC,
Agreed, there is no "actual" need to readback QNH with the ATIS code when checking in with approach. I would say that need there is a genuine need to give QNH on requesting departure clearance etc as not all places give QNH with taxi instructions and this could be the only QNH x-check before departure.
DP,
The CAP413 reference above is the only info I could find on reading back ATIS info, and I can find no explicit instruction the arriving a/c have to give QNH.