It's a long time since I did this stuff myself so I can only tell you what the theoretical answers, based on a very quick look at the books, might be.
ICAO says (PANS-ATM §8.6.2.1.1) Before providing an ATS surveillance service to an aircraft, identification shall be established and the pilot informed. Thereafter, identification shall be maintained until termination of the ATS surveillance service. I've seen different interpretations placed on this text in different countries but the handy one, for your argument, would be that if a handover and formal transfer of id and control is effected for each frequency then there is no situation when 'Before providing an ATS surveillance service...' applies again because the service continues regardless of whichever controller may be looking after the aircraft. Some national procedure manuals that I have had dealings with simply reproduced the ICAO text but others provide more explicit procedures.
Your recollections of the UK sound familiar to me also and UK the manual currently says 'When providing surveillance services outside controlled airspace, a pilot is to be informed as soon as his aircraft has been identified. When operating inside controlled airspace, the pilot of an aircraft need only be so informed if the identification is achieved by the turn method'. So it seems that if an aircraft is in controlled airspace it is rarely going to be told it's identified (I wonder when an aircraft might be given a turn for id in CAS these days!). There doesn't appear to be anything in the UK AIP to advise pilots that they will not usually be advised that their aircraft is identified, which I would have expected, but the UK RTF manual includes a table that does make this clear.
Don't know if any of that helps or adds to your existing knowledge but I would tend to agree with your thesis that it is not necessary and potentially wastes valuable time to keep on telling aircraft something that they will likely assume to be the case within European airspace.