In the end we're never going compete with what Australia can offer financially, but NZ never used to need to. It used to be that many people would accept a lower salary and often even migrate to NZ because it offered a better way of life than so many other places, often including Australia, but presently its questionable of that's still true for a lot of people. That's especially the case if you're in a front line profession like teaching or nursing where the nature of the job means you constantly have to face consequences from increasing breakdowns in other parts of society.
If you take the ratio of teachers to taxpayers(i ballparked it at 70k vs 1.4m) then it costs each tax payer an additional 5c in tax for every dollar we raise teachers wages. I dont think a $1000 tax bump to ensure out children have a good education is that expensive.