Just logic, page-3

The 30% rebate isn't the only thing the government subsidies private healthcare with. Medicare pays significant proportion of doctor fees in the private sector and PBS reduces drugs costs to private hospitals (which health insurers benefit from).

You are wrong that Medicare levy with a small increase will make private healthcare obsolete. Medicare Levy does not cover what costs the government for healthcare by a long way.

People use private healthcare for access, control and choice. Even in other countries around the world where governments do not support private healthcare there are viable private healthcare industries (e.g. UK) - albeit small relative to government healthcare system (e.g. NHS).

Australia is fortunate to have a health insurance system that has community rating.