Some bad ideas never die. Staked through the heart and dowsed in garlic, still they rise. No amount of evidence has killed off a near-religious belief in performance-related pay. Most research finds it useless or damaging, but faith in gut instinct conquers evidence when governments and managers need to believe it. That's how they feel in control against the moral hazard of idleness.

Performance-related pay (PRP) is being imposed on teachers, the NHS, the police and civil service, translated from the private sector – where it forms under 10% of total pay, according to Dr Alex Bryson of the National Institute of Economic and Social Research. Most of that is not in ordinary pay packets, but in the culture of top boardrooms where it is used to justify astronomically rising top pay.

Yet even there, Sir Philip Hampton, the chairman of Royal Bank of Scotland, has punctured the orthodoxy. Addressing a High Pay Centre conference (on Monday), he spoke of having had "an out of the body experience" in dealing with bankers' pay, besieged by those on £4m pay packages complaining things were "very, very unfair" because another bank was paying £6m: "Bankers take the biscuit."

The epidemic of top pay, which he has railed against before, is a symptom of what he called "market failure". Since no single bank dare act alone, he understands why the EU is enforcing a limit of 200% on bankers' bonuses (resisted by the UK government). But here's a paradox: the rules for the RBS chief executive officer's bonus stipulate that 20% depends on satisfactory employee engagement – yet the very fact of a stonking great bonus is quite likely, according to research, to engender deep disengagement from his staff.

Here's another perversity: members of remuneration committees on company boards have had a 14% pay rise, because setting executive pay has become harder with new demands for transparency. Another perversity: transparency itself has inflated top pay, as everyone knows what other boardrooms pay and every company to be in the top quartile of high-status pay.

The excuse is that CEOs are rewarded for success, but Sir Philip and other speakers listed the reasons why, as he put it, "incentivisation is over-rated". A CEO's contribution is impossible to measure: what did he do, what did his team do? Targets change every few months as circumstances change, so setting a long-term incentive plan means hitting an out-of-date target, probably by luck years later. Mediocrity is usually rewarded, bonuses paid regardless: if targets are missed, the criteria are softened. Share prices are a bad guide as they rise and fall with the market – and in a decade when top pay has quadrupled, share prices have barely shifted.

PRP works no better lower down the pay scale. Professor Stephen Bevan, of the Work Foundation, says it rarely achieves its aims and often results are perverse. For Remembrance Day, here's a good example: when the Luftwaffe incentivised its pilots to target Spitfires, its bombers were left unprotected and so shot down in greater numbers. The same perversity is found in banking: Hampton blames the mis-selling of payment protection insurance on pay incentives, resulting in massive sales – and now massive fines. Even good incentives go awry: a Chicago bank incentivised staff to lend to small business, so lending shot up by 47% – but defaults rose sharply too. Adair Turner, then head of Britain's Financial Services Authority, blamed "inappropriate incentives" as a cause of the financial crisis.

That is the culture now expected to deliver better for the public sector because the government "believes" it works. Evidence suggests otherwise. Those rewarded tend to be bugginses or managers' favourites, spreading resentment. It erodes trust, breeds short-termism and rewards the ingratiators, regardless of achievement, according to Prof Bevan. Managers think they know how to evaluate performance, but can rarely define or calibrate it. Teachers are resisting it – with good reason. OECD studies of 70 countries found PRP had no effect on pupil attainment. A Harvard study of New York schools found grades unaffected by it.

Imposing PRP now comes as a double affront to the public sector when pay has been frozen. Prof Bevan's research shows how wasteful this will be, with 95% of management time obsessing over rewards that will be a tiny percentage of pay, causing maximum upset for minimum effect. Unequal pay in schools is rising, with the Times Educational Supplement finding that more than 100 heads now earn over £150,000, with academies' pay hidden from scrutiny.

The only hope is that in a better future people will look back in bewilderment at our post-crash failure to correct dysfunctional rewards. FTSE-100 CEOs on an average of £4.3m reap 160 times the median pay, four times more than a decade ago. Median pay has been stagnant for a decade, with wages falling behind inflation – and next year, according to the FT, set to fall further. Under this government the only month when median pay didn't fall was April, when the mega-paid rushed to take super-salaries, delayed to avoid the 50% rate. That shows how much the "average" is warped by the few obscenely paid. Risk is shifted on to the shoulders of the lowest paid: insecure, zero-hours agency workers whose flexibility ebbs and flows, while top pay rises inexorably, regardless of markets.

Why the obsession with performance-related pay, amid this high- and low-pay crisis? Management by carrot and stick feels effective, even if it does no good. Financial incentives that work best are collective ones, with all staff rewarded together – John Lewis being the classic model. Yet PRP retains a mystical grip on this government, justifying high pay while dividing and ruling the public services.