If they pay you 3k to install a battery, what’s the cost of the battery overall?
Fwiw the reason the ~$6k price point is common in that list is because the rebate is 30% up to $3k including install+inverter. So that's the price point everyone's trying to aim for. You could get smaller systems but may as well maximize that rebate.
Australia's average daily household usage is 15kwh. So 10kwh works well in a country that doesn't need significant night time heating, just daytime (when powers cheap) air conditioning.