Hearing the CEOs of Britain's "too big to fail" banks talk up their annual results in the past few days, it was difficult not to feel a mixture of pity, respect and fear. In particular, the heads of the partly state-owned Lloyds and RBS face demands that are logically impossible to meet, and to see them trying to be everything to everyone almost produces compassion. Their struggles also elicit respect, because they still manage to put on a pretty good show. But then you realise what they can't tell us, and how their bank's failure will be the financial equivalent of a nuclear meltdown, and you shudder.

Announcements of annual results – Lloyds and RBS last week, HSBC on Monday – come with conference calls for financial journalists in the morning and, sometimes, press conferences for lunch. It was interesting to note that the two banks dependent on the government made their top people available for informal chats in the margins of a press conference, while HSBC, which isn't, made do with a conference call at which almost half the time was taken up by the heads reading out a prepared text.

The Lloyds and RBS press conferences were strikingly similar and, as they wore on it became hard not to think of them as dull, rather sophisticated but above all extremely effective rituals. On one side of the table were men (Lloyds had one woman, who said nothing) in suits projecting an image of control. Yes, they were presiding over banks with tens of thousands of employees engaged in very different and often wildly complex activities across the globe. Yes, they had been caught out by scandal after scandal somewhere in their vast empires and yes, in the past their books had given a wildly inaccurate picture of the risks they were running.

But all of this was now in the past and firmly under control, they implied, as they fired off endless numbers and percentages and ratios, and said things like "We remain very confident of our capital position," or "Our strategy remains centred on taking into account the interests of all of our stakeholders", or some other cardboard PR phrase CEOs learn to use when they want to deflect a question they know can't be followed up.

Their vocabulary had been sanitised to a startling degree, with PPI and other schemes that cheated tens of thousands of trusting Britons out of their money becoming "legacy issues" requiring "customer redress". (HSBC referred to its huge fines in the US for massive drug money-laundering as "regulatory and law enforcement matters".)

This was one side of the table, and on the other side were the financial journalists, most of them looking distinctly less well dressed. What to ask when you've only just been given a telephone book of numbers and tables? Excluding three appendices, the RBS annual results came to 289 pages. HSBC produced 550 pages and Lloyds 165. Finding the hidden risks therein wasn't a puzzle in which you look for an answer to a question. These annual reports, and the huge organisations they purport to cover, constitute a mystery, ie a situation where the question itself is unknown.

"What was that £250m for?" asked one journalist. How was the CEO's pay structured? What did Lloyds think of the EU cap on bonuses? The CEOs would address most reporters by their first names, then give a meaningless answer. About a third of the questions focused on the terms and timetable of Lloyds' and RBS's return into private hands; will the taxpayers get their money back?

This was where it quickly became clear that Lloyds and RBS are asked to do the impossible. The holes in their books are caused mostly by toxic loans, but they are told to increase lending, that is to lend to parties they would otherwise prefer not to lend to. At the same time, they must increase their capital buffers, so hold on to the same capital they are told to lend. RBS and Lloyds must increase profits, but are crucified when they pay bonuses to the very bankers who bring in those profits. The banks must also be ethical, so stop the profitable practice of ripping off their clients. Also, Lloyds and RBS must focus on the UK, even though it is almost impossible for a bank to make profits in an economy that is flatlining (HSBC lost money in its UK and US operations, and was saved by its activities in emerging markets). To boot, the UK government intends to increase competition between banks on the high street – a move that ought to decrease margins.

In short, Lloyds and RBS are told to increase profits so they can be privatised as soon as possible, while at the same time being told to stop doing many of the things that traditionally brought in these very profits.

It almost felt as if the RBS and Lloyds CEOs' job was to maintain the illusion that this could be done, while providing a lightning rod to all those who don't want to look beyond bonuses and the question of whether the taxpayers get their money back.

What if bonuses and privatisation are diversions and the real issue is "too big to fail" in combination with too big to manage? If you believe that CEOs knew nothing about the scandals taking place under their watch, what reason is there to believe that this time they are on top of things?

Over the past 18 months I have interviewed more than 150 people working in finance in London, most of them in junior functions. Many of them believe that the top of their organisation has no idea what's really going on. They are equally scathing about the regulators.

This is the debate Britain refuses to have. The timing and conditions of the privatisation of Lloyds and RBS are vital to the British government's financial health, and it makes for powerful and simple-to-produce stories, especially if these banks continue to pay high salaries and bonuses. But Lloyds' and RBS's return to private ownership is ultimately a question of secondary importance when both banks continue to be too big to fail – and so effectively remain a public liability.

While this idea persists, Britain remains hostage to the health of banks over which it has only very limited influence. Knowing that your vital interests are affected by factors beyond your control is a recipe for stress. It's not what democracies should be about. But it has become the new normal. The big issue today is not whether British taxpayers get their money back. It's whether British citizens get their sovereignty back.