The bad smell from the carcass of British banking refuses to disperse.

Just keeping track of the scandals – as numerous as the excuses – is almost a full-time job. A great deal of money left the public purse, directly and indirectly, to preserve an essential industry. The implied moral debt remains. Now we are told there is a very slim chance of retrieving the actual cash.

What do bankers get up to these days? The question isn't facetious. The answer might tell us something important about the nature of 21st-century Britain. After all, if the industry's central function, put simply, is to move money around, the bankers aren't banking.

The mortgage business has shrunk, mostly because of the terms demanded. Small and medium-sized firms complain endlessly that they can't raise loans. Investment banking has been scaled back drastically. Savers and pension holders capable of simple arithmetic know they are being given atrociously bad deals. You can't borrow – the exaggeration is mild – yet it's pointless to save. Where does the banking come in? And why does anyone wonder about Britain's economic difficulties?

The banks have been busy, if it counts as progress, in laying people off. Across Europe the industry has shed 160,000 staff in the last year and a half, and that's in addition to the first wave of redundancies in 2009. It ought to go without saying that many of the victims were ordinary taxpayers, not bonus merchants. By one estimate, nevertheless, the Treasury has been deprived of £30 billion in revenue thanks to their misfortunes. The old boast that the City props up the country is beginning to sound a little hollow.

Still, the recovery is on its way, is it not? Ministers are as clear about that as they were last year, and the year before. Surely we should get at least some of our billions back when things pick up? The US Treasury has already predicted that it will make a modest profit from its own bailouts. On paper, Britain's voters have £66bn tied up in RBS and the Lloyds group. That must be a windfall worth anticipating.

The Commons Public Accounts Committee suggests, instead, that you refrain from holding your breath. Reporting on the debacle of the Northern Rock sale to Virgin Money – a £2bn loss with all the toxic rubbish left in public hands – the MPs speculate that if the Government attempts to flog off its 82% of RBS and its 40% of Lloyds much of the £66bn will never be seen again.

Buyers are few: Virgin had the field to itself, in effect, when it went for Northern Rock. Equally, the state paid far more for its shares in RBS and Lloyds than the shares are now worth. Certain other "issues" still hang over banking, from Libor-fixing to the cost of the great PPI fraud. All in all, the committee is gloomy. Its greatest fear is that George Osborne, the Chancellor, will attempt to sell the public's stakes regardless.

Why would he do such a thing? The short answer is that he did it with Northern Rock and accepted a loss. In that case, however, he had the excuse that EU rules on state aid gave him no other choice. RBS and Lloyds amount to a different case. It would be astoundingly bad business, and ideological nonsense, to dispose of state assets such as these in the foreseeable future. Such is the essence of the committee's view. But why get rid of these banks under any circumstances?

The EU bureaucracy has many powers, and a marked taste for privatisation, but it has not yet got around to banning public ownership. Others banks would be outraged by state-backed competition, but they hardly count as an ethical force just at the moment. Given the choice between losing a bundle and owning banks capable of returning a profit for the public purse, most voters wouldn't hesitate. Yet on all sides the idea is treated as unthinkable.

The history of privatisation since Margaret Thatcher's binge is, to put it politely, mixed. Instead of the supposed vices of the old state industries we have seen farce and scandal time upon time. This week's allegations concerning energy markets and "competition" were so predictable they barely raised an eyebrow. The next controversy involving the railways will be along shortly, no doubt. Yet still nationalisation is beyond the pale.

One favourite argument involves the claim that civil servants can't run industries, and therefore should not try. As rows over rail franchises have shown, there is something in that. But does anyone really need to examine the recent history of banking? Not if they're in search of evidence of competence, efficiency and honesty.

Are customers content with the services provided by banking, meanwhile? If there are such people, I haven't met them. PPI and swaps inflicted on small businesses were two tips, big enough in their own right, of a very big iceberg. Resentment against banks and their charges was smouldering away long before the extent of bankers' folly became obvious. It would require very little luck for public servants to do better.

At Northern Rock, after the bail-out but prior to the sale, the political advocates of free markets decided to leave the management in charge. You could call that naive; I can think of other words. One result was that the professionals managed to fall £6bn short of a £15bn target. Another immaculate performance, as the committee reports, was that "Northern Rock PLC still lost money in 2011, and its strategy should have been challenged sooner". You could say that.

The fiasco was allowed simply because of a blind faith in the idea that no government should ever interfere in markets, and that politicians must always remain at arms' length. If as a society we still believe that we have truly learned nothing at all from the banking crisis. Worse, if we believe the tale we are refusing to recognise that banking remains dysfunctional and worse.

In happier times banks liked to pretend that they existed only to serve. They were our friends; they liked to say yes. In other words, they happily exploited the public sector ethos in order to part us from our money in as many ways as possible. The pretence has been exposed utterly.

Britain is meanwhile patently in need of a nationalised lending bank, ideally one working in tandem with the Post Office. The better building societies remind us that they are "owned by their members". Why should a state bank be any different? Why on earth should it be unthinkable?

Mr Osborne would no doubt give you a fine lecture on his duties and responsibilities. Duties and responsibilities to whom, precisely? If he rushes to sell off RBS and the Government's stake in Lloyds – just before the next General Election would be my bet – the answer to that question will be unambiguous. Then we'll know for certain that the banking lobby is back in charge. By then, a matchless opportunity will have gone.

Margaret Hodge, chair of the Commons committee, predicted this week that we have not seen the last banking crisis. Anyone who shares that view and still refuses to protect the public interest effectively is worse than culpable.