Demand stopping works when your stops are close together, lightly used, or mainly used during peak times. It does have one main advantage in that where you have a high service frequency, it allows trams to skip stops and avoid bunching up. This also allows loadings to be more evenly spread (this could be resolved by using modern larger trams with a greater capacity!).
Removing 25 - 30 % of the stops would go a long way towards justifying this, as would higher density living along tram routes.
The big pickle in moving to such a system is that the network - particularly during off peak times and on sunday to wednesday nights - can be very lightly used at times.
Also, from a motorists perspective, it would add to their travel time and possibly increase (wether real or perceived) congestion around tram stops.
One way to get around this would be to make the system demand stopping during weekends and off peak times, however this would lead to much passenger (and possibly even driver) confusion about wether the tram is going to stop or not.
Ideally, the best way would be to simply make all platform stops compulsory stops - that way in areas where you have mainly non-platform stops and very low loadings, you wouldn't have a problem, and areas like the City and St Kilda Road where there is high and consistent loadings, you would be always stopping.
As previously mentioned, I believe that the main downside of such a change would be a general slowing of tram speeds, as at the moment, if one tram is closely followed by another tram with the same destination, it may skip that stop. It might not sound like much, but it allows loading to be spread over more trams, as well as trams to keep moving. Making platform stops compulsory stops would increase the likelihood of trams bunching up together, especially around the city and other high frequency areas.
There are other issues, but either way, it is unlikely to be changed across the network any time soon. Certain areas might one day benefit from this - such as if all St Kilda road services were replaced by high frequency large trams operating a shuttle service, with other services feeding into it. This is a scenario that has been discussed internally for quite a while, and it is something that (apart from the 'inconvenience' of passengers having to change trams) would lead to a lot of network efficiencies, as well as (if done properly) ultimately a better passenger experience.