Pensions tax relief is a juicy morsel for the chancellor should he find a way to make it benefit the exchequer. Even a small slice of the £38bn spent each year subsidising pension saving could help thousands of schools and hundreds of hospitals that would otherwise be starved of cash.

A £10bn saving is not outside the bounds of possibility, and that is without even shaking the system to its foundations. All Philip Hammond needs to do in his autumn budget is take away the tax relief top-up offered to higher-rate taxpayers and the £10bn a year can be his.

It is a prospect often considered inside the Treasury. And why not, when the people who have benefited the most from this apparently merciful and most charitable form of state aid are the richest in society?

It is commonly agreed that around 40% of the £38bn goes to the top 10% of earners, which in today’s money includes all those who earn £70,000 a year or more. That’s a massive bung to the better-off and one that is difficult to justify. There is no reason why someone on the average salary of £27,000 a year should receive 20p in the pound from the government to support their pension saving and someone on £47,000 get 40p.

It’s true that they pay tax at these respective rates. And it’s true that the calculation is made easy when the benefit to the taxpayer tallies with the rate at which they pay tax. Yet ease of calculation cannot be a good reason for determining how much support the state offers pension savers. The days of paper ledgers are long gone. There is no excuse. Not even from a tax authority straining under staff shortages.

Tax reliefs share the same​ thinking, which is that people won’t do the right thing without a ​​huge bung from the state

Why, then, does this obvious source of revenue elude one chancellor after another?

One reason is the impact on the £2 trillion-plus locked up inside private- and public-sector final salary pension schemes. They have built in to their calculations the higher level of state support for better-paid workers. If it is taken away, their deficits increase dramatically.

Then there is the problem that the people who would be most affected – the better-off – are also among the most vocal. They pose the same problem when governments consider increasing tax on land and property. They are the owners of property and the owners of pension rights. The message is that any minister who devalues these assets does so at their electoral peril.

And what if the chancellor succeeds in withdrawing tax relief? Will the better-off go on a pension strike? In other words, will they cut back on how much they put aside each month if the government’s help is reduced?

It’s not an academic point. In other areas where subsidies apply, the decision to reduce or withdraw them often leads to a drop in activity, especially when the activity is investment-related. Solar-panel subsidies are a case in point: when the amount of subsidy per kilowatt-hour was reduced, putting solar panels in a field or on a roof was no longer considered a top investment. The solar industry went into freefall.

No chancellor wants to preside over a drop in pensions saving, even if it means that the money is spent on the high street instead and the Treasury not only saves money subsidising pensions, but gets some VAT as well.

Yet Hammond should reform pensions tax relief. There is no justification for handing a bigger subsidy to higher-rate taxpayers. It is an arbitrary system that says someone earning £47,000 deserves more support than someone earning £45,000 (the salary at which earners start paying higher-rate tax is £46,351).

The Resolution Foundation wants the chancellor to go further and question the entire roster of tax reliefs on offer, which it says added up to £155bn in the last financial year. Last week it highlighted entrepreneurs’ relief, which cost £2.7bn last year. It described the scheme, which allows people selling companies to pay half the normal rate of capital gains tax (10% rather than the current top rate of 20%) on up to £10m of gains, as “expensive, ineffective, and regressive”.

That same damning criticism can be levelled at pension tax relief and most others on the list. They either enrich wealthy individuals or successful companies. Tax relief on research and development is mostly claimed by the big pharma companies: most small and medium-sized firms don’t get a look-in.

And they all share the same underlying thinking, which is that people won’t do the right thing without a huge bung from the government. More specifically, that the better-off won’t go to work, be innovative or save anything for their retirement without government subsidies.

It’s time to call their bluff.