Apples and oranges.
In those days the Navy had: OS and LS
and the Air Force had: AC and LAC
and then the Army had: Pte and LCpl
just for starters.
Tell me this would be easy to keep straight in a "Unified" force.
The three examples you cited, George, don't quite fit.
Leading Seaman in the RCN was the equivalent of Corporal in the army and the RCAF.
However, a Leading Aircraftsman was the same as Able Seaman in the RCN and Private (and all the others) Trained, Higher Rate in the army. The difference was that the others services did not have a distinguishing badge, while a LAC wore a horizontal propellor on each sleeve.
The other services did not have an appointment (not a rank) similar to Lance Corporal. A unit could appoint 12.5% of the privates to Lance Corporal. It was used as a stepping stone and a means of assessing developing young soldiers. If posted, a Lance Corporal reverted to Private.
Still, it would not be beyond most of us to learn more than one system of badges of rank.