Romeocharlie,
No everybody doesn't, several AU operators have( or are in the process) moved their cadets to the MPL system, a sensible move for an airline.
To be clear, an MPL is tied to a sponsoring airline, and is integrated with that airline's SOPs from the start of training. To swap employees within an NAA territory would be entirely a matter of negotiation with the local authority. Going over national boundaries would, I rather suspect, be as near as impossible as I can imagine. That goes double if CASA is involved. Just look at the roadblocks various NAAs erect to the conversion of other license types, if they are more than a PPL.
If you hold an MPL from an issuing NAA, once you get the ATPL/ALTP hours, that (NAA's) license can be issued, there are no further course/exam requirements.
Once you have the ATPL/ALTP, you are no longer tied to the sponsoring airline.
Tootle pip!!