The main disadvantage for the self-funded is that the MPL locks you in to a particular type fairly early, ie MPL gained in B737 simulator is no use for A320. So the sponsor airline - if there is a sponsor airline - needs to know well in advance its crew and fleet forecasts.
The main disadvantage with our present system for the direct entry airline cadet is that a lot of time is put into developing single-pilot IFR skills just to get through the command instrument rating, then much of the one-man-band stuff has to be unlearned quickly. Also, some light twin techniques are negative learning for immediate transition to jet operations e.g. the need to be quick on the draw when shutting down an engine for fear it won't feather, or worse, won't fly.
For those countries that don't have a large enough GA industry to use as a training ground - ie most of the world outside Africa, Australia, the USA and Canada - the MPL makes more sense than the existing system. If the Australian training industry or CASA ignores this fact, we will miss out on a lot of future earnings.
For those countries that do have a large enough GA industry to select pilots from, I hope airlines continue to use it for what it is worth. There is no substitute for experience.