I always enjoyed catching up with the L on the Sunday zoo service when visiting Melbourne, being particularly fond of the sound of Spur gears, but as far as I know its demise was not particularly the result of the City Circle service, but if it was still running when that latter service commenced, it could well have been a factor.
As I heard, it was the difficult logistics of operating the L. Essendon Depot had been an Z/B class only depot for a while, and at the time if a driver did not drive a hand-controlled car for a specified number of months, he was considered unqualified to operate this style of tramcar, and would have to at least have a refresher course. I think that it was after 12 months the qualifications lapsed altogether and the person was considered a new student required to perform their 96 hours of training all over again, even if still qualified to drive foot-control trams. After a while, new Z drivers were never taught how to drive Ws unless they went to a depot where they would be required to do so.
The other aspect of this is that while the service was a welcome addition to the slim double-time Sunday roster, as time went on there was less desire to make sure that the L class was operated. For most drivers the more comfortable Z class was much preferred, and if the L was up the back of a depot road, even the very short Essendon depot road, it was sometimes considered too much trouble to shift a couple of trams ahead to let it out. So a Z ran the service.
So with the passage of time, with fewer drivers eligible to drive the L, and less desire to run it, the decision was probably made that the original purpose of the service was gone (an excuse to run a vintage tram) so the entire shift, I expect, was deleted.
The other often forgotten, and largely unknown vintage car service was the running of V 214 on summer Sundays, X2 676 in the winter, from Batman Ave to, i think, Hawthorn near the depot. Coming from Camberwell, the crew qualifications issue with the passage of time was probably a factor, not overlooking the extra '2- Motor" qualification needed for those two cars.
In both cases, staff moving on would also thin the ranks of qualified drivers.
Greg King could well know more about this, and maybe other list members.