This is only partly true. The deregulation didn't make things a whole lot cheaper for taxpayers it just made it possible for private owners to profit massively.
The concept that we aren't prepared to pay for more seems incorrect to me as well. It has taken a Royal Commission to highlight how underfunded the sector is and how bad the levels of care have been. It takes a government to decide that this is the level of care that needs to be mandated and this is the cost and to budget for it.
To add to this, the Government's contribution is based on a score of each resident's care needs, using a tool called the Aged Care Funding Instrument (ACFI).
ACFI is used across resi care settings, regardless of ownership/profit model.
To generalise, public providers generally attract lower ACFI scores across their centres despite having far higher resident acuity levels and care needs. You can attribute this to a staff unwillingness to "game" the system.
Private providers are known for employing ACFI managers whose role is largely to ensure maximum funding can be squeezed out of each resident, within the rules.
Hospitals employ staff to do the same thing with the annual pricing revisions.
So when aunt Jude is given the option between the low price shabby public home and the glossy catalogue private home, the core component of Government subsidy is potentially the same. If she choses the catalogue home she'll be getting nicer carpets and meals/entertainment, but likely at the expense of a trained nursing workforce.