Yes, obviously medicare would need to increase the rebate and private insurance fees would necessarily increase(as they would now be actually paying for care rather than acting a a gatekeeping mechanism)
Rebate for a short consult with a specialist is $81.55, a long consult is $236.65.
The title professor indicates that they hold a teaching position and says nothing about their clinical skill. Plenty of specialists take the piss and leverage the title to charge ridiculous fees.
In my experience as a GP a reasonable standard fee for a specialist is around $300 with $80 back from Medicare. So yes the Medicare rebate would need to increase substantially but I doubt more than we will save when AUKUS falls through. It is within the capacity of a government with the right priorities. Also increasing the availability of public specialists would be a good companion policy.