I would say that it was relatively common. I've seem it many times and not only following the disbandment of the CAR and not only involving the wear of that regiment's badge. In the 1970's, one of the MCpl Med As who was posted into 1 Fd Amb had been infantry (PPCLI) before he remustered and had served in the CAR - he wore the CAR badge inside his beret. At the same time there were other Med As who had previously been other trades (usually infantry) who wore badges of their former regiments (QOR, PPCLI, RCR) similarly inside their berets. There were also a number of Med As (as Med Techs were called in those days) who did the same following their service in the CAR where all trades wore the same cap badge. I even knew of one person who had served in 3 Mech Commando (in Germany), was not jump qualified, but wore his CAR badge inside his beret.
In a similar vein, when I was going through infantry phase training I wore a combat cap (but never in the Robin Hood style) that had the medical badge on it, however it was not as homage to my former (and later returned to) branch - it was just that the badge had originally been glued to the cap - gun tape solved the problem of covering up the badge. On the only occasion when one of the instructors questioned what was behind the gun tape, his response to my explanation was to show me his beret that had the QOR badge inside behind his PPCLI badge.