After this week's events, they look rather less independent than they did. Something of the myth has been stripped away. The extraordinary lengths to which the Conservative whips went to remove Nicholas Winterton, the fiercely independent and happily maverick MP for Macclesfield, from the health select committee, have exposed something that has always existed - the whips' influence on who sits on the committees.
'A bad day for Parliament,' was not just the verdict of Mr Winterton, and Frank Field, the Labour chairman of the social security committee, who attempted to rescue him. The same was implicit in the criticisms of Sir John Wheeler, the loyal former Conservative chairman of the home affairs select committee, who was required to fall on his sword as a result of the three-Parliament rule used to oust Mr Winterton, and of Sir Terence Higgins, the former Tory chair of the treasury and civil service select committee.
The result of the new rule, Sir John said, was like stepping on bubble gum: 'tacky, sticky and lingers long after the event'.
'A repair job is needed,' said Lord St John of Fawsley, the former Norman St John Stevas, who as Leader of the House set up the departmental select committee system in 1979, holding a reluctant Margaret Thatcher to a manifesto commitment to introduce them. The committees were, he said, 'a crucial backbench check on the executive'. They had been set up 'because the Government had become more and more professional while the House of Commons had remained amateur'.
Question Time, originally designed as a backbench scrutiny over the executive, had turned increasingly into gladiatorial combat between the parties, he said, 'and you cannot at Questions follow a sustained line of questioning to provide an effective supervision of policy - whereas you can in a select committee where the atmosphere is non-partisan'.
The choice of who sat on committees, Lord St John said, had deliberately been put in the hands of the cross-party Committee of Selection, not the whips, because while it was inevitable that the whips would have some say, they should not 'run and manipulate the whole system'. What had happened, he said, was 'damaging to the whips and damaging to the select committee system'.
The committees' credibility, he said, 'needs to be restored'. One answer, he suggested, was for the Committee of Selection to find itself a new and 'totally independent chairman' to replace Sir Marcus Fox, the newly elected chair of the Tory backbench 1922 committee, whose reputation has been tarnished by the furore, a chairman who would 'ensure the rights of Parliament'.
Some MPs believed yesterday that the system's credibility may have been permanently damaged by the row - a credibility, some MPs suggest, that had not been helped by Tory committee chairmen seen as 'loyal' receiving knighthoods in the recent honours list, while Kenneth Warren, the pugnacious former chair of the trade and industry committee, received nothing after the committee's investigations into the Iraqi supergun and Rover sell-off.
However, Lord St John believed the system would recover. Once the committees started operating, he said, their culture would reassert itself. 'It is like Henry II and Thomas a Becket, or Mrs Thatcher and John Major,' he said. 'The beast asserts its own independence.'
So why did the whips try to fix it? 'Oh,' Lord St John said, 'because the whips are fixers'.