Good day
Swiss banks have become less welcoming of customer residing outside of Switzerland in recent years. This has affected non-resident Swiss citizens as well. The deciding factor is not your nationality, but your place of residence.
Most Swiss banks charge non-resident customers additional fees. This markup averages 300 francs per year - some banks charge less, some charge more. Some banks waive non-resident fees in special cases (for customers with mortgages or assets under management at the same bank. You can find more information here.
From a purely cost vs. return perspective, holding a Swiss bank account as a non-resident is hardly worthwhile due to the poor interest rates and high non-resident fees.
If you would like to open a Swiss account in spite of the drawbacks, you can use the unbiased moneyland.ch account comparisons to find the most favorable accounts. You can then contact the relevant banks and ask them about non-resident fees for customer residing in Australia (these fees are not shown in the comparison).
Best regards from Moneyguru
More on this topic:
Swiss Bank Fees For Non-Resident Customers