Having embraced their brief, they then desire to dominate it. And here they become somewhat frustrated.
Arts policymaking is stuck in a 1946 timewarp. It was then that the Arts Council was set up under the chairmanship of John Maynard Keynes, and it distributed cash annually to its theatre, opera, music and dance clients. When arts ministers were invented some time later, they merely negotiated the sum from the Treasury for the Arts Council to distribute. The "arm's-length principle" was born.
I remember a frustrated David Mellor, when he took on the portfolio, telling me he was damned if he was going to use all his skills to wheedle money out of the Treasury for the arts, then have no say at all in how it was spent. But he did not manage to beat the system.
Last night, in a lecture to the Royal Society of Arts entitled "Our Culture, Our Heritage", Virginia Bottomley decided to chance her arm. First, she proved her devotion to contemporary culture. The bastion of home counties Conservatism cited as world renowned sculptors and painters the unholy conceptualist trinity of Damien Hirst, Anthony Gormley and Rachel Whiteread.
"It is part of my role to create a framework in which the experimental will be supported," she said. "Whilst work which sets out merely to shock, or be a sensation, is unlikely to endure, when artists simply reflect consensus we should worry for the state of our arts."
Like a mum who hums Oasis to show her worldliness to her children at the tea-table, Mrs Bottomley likes dropping the odd subversive name. In similar fashion she very publicly went to see the film Trainspotting at the Cannes Film Festival -- on the recommendation of her daughter - and very publicly loved it. She did not, though, sing its praises to the Conservative Party Conference last week.
Don't read too much into this. Mrs Bottomley is a politician first, and connoisseur of modernism thirty-first. As an aide told me yesterday, she hasn't actually seen that much of the work of Hirst or Whiteread. It was more their general importance than a personal preference: the importance being economic importance - they do well abroad.
In the case of Mrs Bottomley, going native has a calculated political aim. With her audience last night softened up by her one-line espousal of cows pickled in formaldehyde, she began to move towards her real target, the arm's-length principle. Elliptically, she noted that the scale of change since 1946 "has wrought a world that Keynes would hardly recognise".
Less elliptically, she went on: "With the memory of the German, Italian and Russian regimes of the Thirties still fresh in everyone's mind, there was surely no alternative to an arm's-length principle in 1946. But is it still valid? Should we examine it again?"
And then, casting ellipticism to the wind, she announced she was setting up a forum comprising businessmen and women and civic leaders to advise her on a monthly basis.
Is this taking arts policymaking away from the "luvvies"? It certainly sounds like it. "I want to make the holder of my office a more powerful catalyst," she told me recently. Certainly, last night she was being catalystic in all directions - firing broadsides at the Arts Council, and later announcing a lottery award for dance and drama students, though she does not technically give out lottery awards (that, too, is meant to be the Arts Council).
Perhaps this is a liberating piece of pre-election muscle-flexing by Mrs Bottomley. But if she is indeed signalling the end of half a century of government at arm's length in the arts, is it any longer such a heresy? The Government does not run the health or education services at arm's length. Why should there be such coyness over the arts? The answer always offered is, give the minister his or her head and he or she will be decreeing what we can read, watch and listen to. The spectre of Tory Heritage Secretaries censoring subversive arts is actually as remote as a Labour minister refusing to fund a Terence Rattigan season because it is too staid.
As it happens, the only recent example of censorship was not by the government but by the Hayward Gallery - progressive institution that it is - in showing to Scotland Yard pictures from the Mapplethorpe catalogue before its Mapplethorpe retrospective, and bowing to advice on what it should and should not show. (I have to admit I do not recall that champion of the experimental and challenger of the consensus Virginia Bottomley challenging this decision.)
It is the Arts Council, too, that has failed in recent years to resolve funding crises in regional theatres and London's symphony orchestras, while handing out millions of pounds in lottery cash to causes that have not always struck the country as wholly deserving.
And it is the same Arts Council whose own Byzantine procedures leave government, even this government, looking like democracy incarnate. Who elects the Arts Council and its advisory panels? Nobody. It is a quango of largely like-minded people who stare incredulously if you suggest that some of their procedures may not stand the test of democratic purity.
Is it acceptable that the chairman of the Arts Council's lottery panel recommends a multimillion-pound award to the Royal Opera House, then takes over as chairman of the Royal Opera House? Is it any more acceptable that the architect behind the South Bank redevelopment, also funded by a multimillion- pound lottery award from the Arts Council, is the vice-chairman of the Arts Council? No rules broken, but wouldn't we demand more rigorous standards from an elected minister of culture?
George Orwell and the experiences of totalitarian countries have engendered in us a distaste for the idea of a cultural affairs ministry with real enabling powers. But, unlike the Arts Council, such a ministry would at least be publicly accountable.
We also need something more substantial than a nodding gesture towards Damien Hirst or a daughter's recommendation to see Trainspotting to demonstrate the catholic tastes of the serving minister. Rather than plucking a few tabloid cultural demons at random to give herself street cred, Mrs Bottomley and future Whitereads and Hirsts would be better served by her new advisory forum informing her of who is doing the most challenging and innovative work.
She could also change the practice of funding institutions rather than people, which meant that Peter Brook, an idiosyncratic, but much-admired, director, had to go to Paris to run a theatre company.
Provided we have first-rank ministers and civil servants, we have nothing to fear from a Ministry of Culture. What we do need is an end to the elliptical hints about the changes in Britain since Keynes bestrode the arts. The Government should announce whether or not it is going to abolish the arm's-length principle and with it the Arts Council. Then we can begin the real debate about the nation's cultural policy.