Yet events seem to be moving in the opposite direction. Mr Waldegrave is responsible for five research councils that channel more than pounds 1bn of the taxpayers' money to support basic science. Two of them are no longer to have full-time chairmen.
On Friday, Professor John Knill came to the end of his term as chairman of the Natural Environment Research Council (NERC), and no full-time replacement has been appointed. In December, Sir Mark Richmond, head of the Science and Engineering Research Council, will take up his appointment as director of research for Glaxo, the pharmaceutical company, and will continue only part-time at the SERC.
Research councils are difficult to run at the best of times, but they face reorganisation and change unprecedented since the 1965 Science and Technology Act brought them into being. If they needed full-time chairman in normal times, how can they do without full-time direction now?
Mr Waldegrave is planning to add a new tier of bureacracy to the administration of science. The scientists who currently serve as chairmen of the research councils will be demoted to the role of chief executives (although they will be paid more than at present) and new, part-time chairmen will be brought in from outside the scientific community. When the new arrangements take effect in April, Sir Mark Richmond, for example, will have two replacements: a chief executive and a chairman. Yet the administrative burden is most acute now, not in April.
Rumour has it that the salary for the NERC's new chief executive will be some 25 per cent higher than before. A simple, back-of-the envelope calculation suggests that in direct salary costs alone, Mr Waldegrave's reforms will cost the science budget at least pounds 300,000 a year more. Superannuation and other costs will double the figure.
Yet the science budget is so tight that the SERC refused Sir Geoffrey Wilkinson, the Nobel Prizewinning chemist, pounds 30,000 for his research.
Mr Waldegrave also intends to create a new research council. The salaries of its chief executive and chairman will be a further charge on the budget. To add to the complexity, Mr Waldegrave has dreamt up a new (and expensive) full-time post: director general for the research councils, to oversee the chief executives.
Perhaps these new and previously unnecessary administrative costs go some way to explaining the departure from normal practice last month, when Mr Waldegrave's department published the massive compendium of statistics which constitute the Annual Review of Government Funded Research and Development.
The story buried in this tome is one of failure: unless there is a massive hike in science spending next year, the Government will be devoting pounds 1bn a year less to research and development than it did a decade earlier.
The annual review is a complex document and easy to misinterpret. In previous years, before John Major created a ministerial 'product champion' for science with a seat at the cabinet table, the Cabinet Office would do its best to help journalists through the complexities of the document. It would be distributed, under strict embargo, before publication so that reporters could actually read it, and then, at an informal briefing, statisticians would go through the details.
In addition to his responsiblities as product champion for science, Mr Waldegrave is minister for open government. What a splendid opportunity to display the Government's commitment to openness, by the minister himself attending the press conference.
But there was no press conference; not even advance notice of publication. It looks like a classic case of government media management to minimise bad news. The report thus represents a double failure by Mr Waldegrave: its content reveals the hollowness of the Government's commitment to science; and the handling of its publication the hollowness of its commitment to openness.