Here is a prediction. As MPs and commentators contemplate the various ailments that have recently afflicted the government – from embarrassing but essentially unimportant pratfalls to much more substantial problems with tuition fees and health reform – it will become increasingly fashionable to suggest that David Cameron ought to resort to a traditional remedy. The prime minister will be told that a cabinet reshuffle is the way to put some pink back into the government's pallid cheeks.

Calls for a reshuffle will have a willing echo chamber in the media: many a blog, news story, TV piece to camera outside Number 10, radio discussion or commentary can be fashioned from debating the misadventures of hapless minister X and contrasting them with the promising prospects of confident minister Y. For those ministers marked with the black spot, this threatens a very unhappy period until the blade falls on their necks or they find themselves reprieved. For those politicians tipped for ascent, this will be a very nervous period until the call comes through inviting them to Number 10 or the phone fails to ring.

Rumours of an imminent cull will be fed by those Conservative and Lib Dem MPs who think that their outstanding talents are not being sufficiently recognised in the current ministerial rankings. Those tantalised by the prospect of promotion will find it hard not to encourage journalists to propagate the case for "fresh faces" to reinvigorate the government. If reshuffle speculation gets intense enough, it can become a self-fulfilling prophecy. The prime minister eventually feels compelled to have a reshuffle for no better reason than fear of looking like a wimp if he doesn't.

Macbeth may be quoted. "If it were done when 'tis done, then 'twere well it were done quickly." David Cameron will be told that he must not only act ruthlessly to amputate ailing ministers, but also swiftly. I can see reshuffle clamour reaching a peak in early May, in the run-up to and aftermath of the local elections and the referendum on voting reform.

So before everyone says it, let me be among the first to declare that the prime minister ought to set aside some time during the Easter break to weigh up the pros and cons of reconstituting the cabinet. Having considered it, if he cannot find an absolutely compelling reason to do it, he should resolve not to have a reshuffle. And then, before the speculation becomes so intense that it overwhelms his first resolve, he should make it clear that there will not be one.

Prime ministers hold reshuffles for several reasons – and they are nearly all bad ones. Quite often, it is simply a desire to demonstrate, by wielding the ultimate power of hire and fire, who is the boss. There is a school of thought that Mr Cameron needs to be a bossier prime minister. The criticism, mainly to be heard from his own side, is that he has been too much the hands-off chairman of the cabinet and not enough its omni-interventionist chief executive. As a result, when ministers mess up and things go wrong, it is late in the day when he intervenes, as he has just done by enforcing a "pause" on the health reforms. That can be a downside of his prime ministerial style. Broadly speaking, though, it is still to be preferred to being a control-freak prime minister who obsessively tries to micro-manage all his colleagues only to end up driving them and himself demented. In Gordon Brown, we have recently had a case study in how that prime ministerial style leads to the obverse of well-ordered, competent and successful government.

In theory, the reshuffle is a dramatic way for the prime minister to stamp his authority. In practice, it often brings attention to weakness. The epithet "Night of the Long Knives" was mockingly given to the reshuffle of July 1962 when an earlier Conservative prime minister, Harold Macmillan, reacted to adversity by sacking seven members of his cabinet. This did not turn him into a decisive leader. It made a prime minister with a previous reputation as an unflappable charmer look like a panicker who would sacrifice his friends to try to save his own skin.

Reshuffles create new enemies for a prime minister among the sacked and foment alienation among those who have not had the promotion that they were sure they deserved. As a result, many a prime minister starts with the idea of executing a bold reshuffle and ends up tinkering to little purpose. Reshuffles tend to emphasise not the power of the prime minister, but the constraints upon him.

Mr Cameron is additionally constricted because he presides over a coalition government. A delicate balance has to be preserved both between the Tories and the Lib Dems and between the different wings of the two parties. Even those panting for a reorganisation of the government have no expectation that the prime minister would make a change at the three big offices of state: George Osborne at the Treasury, William Hague at the Foreign Office and Theresa May at the Home Office are all regarded as utterly safe. There would be no logic to shuffling Michael Gove from education or Iain Duncan Smith from welfare when they have only just embarked on reforms that are central to the government's ambitions. Liam Fox has made some serious enemies in high places, but it is hard to fire a defence secretary when you are at war and it would be provocative to the Tory right. Ken Clarke is regarded with visceral hostility in Tory tabloid land, but moving against the justice secretary would unbalance the cabinet and alarm the Lib Dems.

An especially bad reason for holding a reshuffle is to stage a bit of a diversion. I can see that the government might well feel in need of one in early May. The results of the local and devolved elections are unlikely to be a resounding electoral triumph for the coalition parties. The outcome of the referendum on voting reform is potentially explosive for one of them whichever way it goes. A No vote will cause tremors under Nick Clegg. A Yes vote will see members of his own party accusing Mr Cameron of making a catastrophic mistake when he conceded the referendum in the first place. My guess is that a win for AV will cause more trouble for Mr Cameron than defeat would mean for Mr Clegg. A reshuffle might divert the media – for all of 24 hours or so. As for the public, the voters are rarely impressed by the ups and downs on the Westminster snakes and ladders board.

There is only one good reason for letting some blood. That is to clear out those ministers who have proved incompetent; those whose disloyalty deserves punishment; those whose credibility is shot; those who have lost the respect of the professional groups they deal with; and those who have become too unpopular ever to win back the confidence of the public.

Andrew Lansley is clearly in trouble on some of those criteria. Does Mr Cameron need to find himself a new health secretary? How the prime minister answers that question really depends on what he intends by the intermission in the NHS legislation. If this is a fundamental rethink which will lead to the abandonment of much of the Lansley Plan, then the prime minister will need a new health secretary. Mr Lansley will be beyond furious and might well resign rather than accept that his masterplan has to go back to the drawing board.

If the prime minister has a different intent, if he aims to tweak the plan to make it more sellable, but not to alter its essential thrust, then he ought to leave Mr Lansley where he is. The health secretary appears to be the only person in government who truly understands his plan in all of its elaborate and contentious detail. To sack the architect but carry on with the plan under someone else who didn't create it and wasn't sure they believed in it would be the worst of all worlds.

Cases are made for moving or disposing of some other members of the cabinet. A more emollient figure than Eric Pickles – who could start a fight in an empty room – might reduce the levels of animosity between the government and local councils. Caroline Spelman is among the walking wounded after the fiasco over selling off forests. But Mr Cameron has to ask himself whether making relatively small-scale changes to the lower ranks of the cabinet would be worth all the consequential disruption to the government caused by a round of ministerial musical chairs.

Tony Blair was a terrible fidget with reshuffles. As a result, the average tenure of ministers fell to just 18 months, which is pretty much exactly how long it takes for a basically competent minister to get a grip on civil servants, understand policy areas and create relationships with interest groups. Under Mr Blair, the typical minister was just getting on top of the job when he lost it or was moved elsewhere. So unless David Cameron has something truly dramatic in mind – and I don't believe he has – he should resist those urging him to reach for the quack cure of the reshuffle. It would not be the answer to the government's problems; it would be a futile distraction from properly addressing the questions.