The latest release of figures of household incomes, spending and savings reveals that the share of total income held by the richest 20% of households remains at near record levels, but that so too does the level of income tax they pay. However, more than anything, the figures highlight the need to resist reductions in taxation and associated government spending on vital services. They show the delivery of public health and education reduces inequality the most effectively.

In the last financial year, new figures from the Bureau of Statistics have revealed that the richest 20% of households accumulated 47.5% of the total before-tax private income. This figure, which excludes government cash benefits, is the second-highest share to go to the top 20% this century:

At the same time the share of income tax paid by this wealthy segment of the population has also remained at high levels. The richest 20% paid 59.2% of income tax in 2017-18, down from the high of 61.3% in 2013-14, but still above the level they paid 15 years ago:

But while such a tax share will no doubt have the flat-taxers up in arms – and certainly is a level that will be reduced if the government’s legislated income tax package remains in place – what the figures show is just how little the level of tax paid directly goes towards reducing inequality.

There are essentially three ways the government seeks to redistribute income. The first is taxation. In 2017-18 this saw the average private household income of those in the top 20% go from $325,412 to $254,822, while for those in the middle-income quintile, their household incomes went from $110,638 on average to $95,980 after tax.

The next way the government redistributes income comes from what they do with those taxes. First there are cash benefits (Newstart, family tax benefit, the age pension etc) and then there are “social transfers in kind”. These are essentially the dollar value of things like education, the pharmaceutical benefits scheme and other health spending. The combination of these benefits significantly reduces inequality by more than income tax does.

While income tax reduces the wealthiest 20% share from 47% to 45%, the addition of cash benefits (which mostly go to the bottom two income quintiles) takes the share of the wealthiest down to 40% and then social benefits in kind reduce it to 35%:

The redistribution is mostly from the top-income quintile to the bottom two – there is actually little change in the share held by the third and fourth quintiles – a bit of a reduction for the fourth from 24% to 21%, which the middle quintile sees its share rise from 16% to 18%.

Thus while income tax reduces the top-income quintile’s share by 2.5% points, the cash benefits reduce it by 4.5% pts and the social benefits in kind take another 5.2% pts:

Thus, because our split of private income is so unequal, it remains vital that we have a progressive income tax arrangement in place, not only to reduce inequality but to ensure there is enough revenue to spend on benefits and services that do most of the heavy lifting to reduce inequality.

And remember the importance of social transfers in kind is not that they only go to the poor – they don’t, we can all receive them – but that they are so vital to those on lower incomes.

While the poorest-income quintile gets 34% of cash benefits, they get just 21% of total health transfers in kind while the wealthiest get 17%:

While this does smack somewhat of a poor spend of money, it reinforces the universality of things such as healthcare and education – and also ensures public education and health do not get reduced to “pity status” wherein as they are seen only as the preserve of the poor, and the services decline.

But the real value of the social transfers in kind become clear when we look at how much they are worth compare to people’s incomes.

Take health consumption. The poorest quintile spend 10% of their gross disposable income on health, compared with 4% by the richest, but while the richest get just 5% worth of their disposable income in health transfers, the poorest get the equivalent of 30% of their post-tax income from them:

Without those transfers those households would be utterly ruined by health costs – and our society would be very much split into the haves and have-nots.

Thus while the poorest do receive a significant amount of their total income from cash benefits, nearly half of their total disposable income comes in the form of these social transfers:

And the reality is that such benefits are becoming more important as the government cuts cash benefits and tightens access to them.

In 2003-04 the poorest quintile received 41% of their total disposable income from social transfers and 36% from cash benefits; now they get 45% from social transfers and just 28% from cash benefits:

And it is here we see the next fight against inequality.

The attack on welfare over the past decade or more has seen a massive level of stigma attached to those who receive government cash assistance, and the implication that it is wasted money (unless of course it is for the aged pension). But as the government attempts to move towards a flatter income tax regime, which will significantly reduce the level of taxation raised, the stigma of those receiving government services will become the next line of attack.

Given how vital those services are not just to the lives of those who receive them, but the underpinnings of our society and their role in reducing inequality, it is a fight that cannot be afford to be lost.

• Greg Jericho is a Guardian Australia columnist