The changes took effect on Friday.
NSW Premier Dominic Perrottet, who led the campaign to ditch isolation rules, believes people will continue to register virus diagnoses.
"We're moving to a system of good faith where people are looking out for each other and caring for each other," he told reporters.
"I just want to make the point ... people should still test.
"We may have further waves of COVID in the future - in fact, we probably expect that. So by testing, you're looking after yourself, looking after your family."
Australia will move to a workplace health and safety regime, with the decision made off the back of lower case numbers, South Australian Health Minister Chris Picton said.
"However, the message is still the same in making sure you're staying home if you're sick and being very conscious of people who are vulnerable in our communities," he said.
The state's chief health officer said she had no doubt the community would be able to take individual responsibility.
"There's been such a fantastic response throughout the pandemic with people following health advice," Professor Nicola Spurrier said.
"Quite often we didn't have things as legal directions and people still did them. I am very confident that will continue over the next month."
The Australian Medical Association wants the government to consider bringing back COVID-19 isolation requirements if cases spike during holidays.
President Steve Robson said information from the northern hemisphere showed newer variants wouldn't be affected by immunity from previous infections or vaccinations.
Australia recorded 36,790 COVID-19 cases and more than 270 deaths last week.
WEEKLY VIRUS DATA BY JURISDICTION
* NSW: 11,900 new cases, 37 deaths
* Victoria: 8061 new cases, 46 deaths
* WA: 4859 new cases, six deaths
* SA: 2512 new cases, 11 deaths
* NT: 249 new cases, no deaths
* Tasmania: 691 new cases, one death
* ACT: 657 new cases, no deaths
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