This is because doctors and health care professionals can’t be in two places at once – studies have shown that introducing private financing does not result in more hours being worked or more care being delivered but simply a shift in services to the most profitable patients.[i]
When countries like New Zealand and the United Kingdom opened up public health care to private payment, adopting a ‘two-tier’ system, resources and health care professionals were diverted away from the publicly-funded sector, resulting in an erosion of the quality of care[ii].
Similarly, in Australia, private duplicative insurance was encouraged with the goal of reducing wait times, but in fact wait times in the public sector did not improve; in areas where private health care was most used, wait times in the public system went up.
In Australia, where about 45% of people hold private insurance policies, those with private insurance are treated faster in public hospitals than patients covered under the public health care system (42 day wait for public patients v. 20 days for private patients for elective surgeries).[iii]
[i] Woolhandler S, Himmelstein DU. Extreme risk: the new corporate proposition for physicians [editorial]. N Engl J
Med 1995: 333:1706-8.
[ii] Minister Ramsey cited in “Written Submissions of the Coalition Intervenors,”  2019.
[iii] https://www.theguardian.com/australia-news/2018/may/24/public-patients-waiting-twice-as-long-for-elective-surgery-hospitals-data-reveals; https://www.theguardian.com/australia-news/2017/may/17/private-patients-treated-faster-in-public-hospitals-than-public-patients-data-show