If Jørn Utzon had been left to finish his masterpiece it would have been more beautiful, more functional and less costly

A giant birthday cake sits on the Sydney Opera House forecourt to celebrate its 40th birthday. Photograph: Lisa Maree Williams/Getty Images

There is a persistent, some would say scandalous, myth about Jørn Utzon and the reason he resigned: that he did not know how to finish the Sydney Opera House. It is best exemplified by an unattributed quote dated February 1962: ''Lying on a beach in Hawaii, Utzon says to Jack Zunz [deputy engineer on the project] that he doesn't care if the Opera House is never finished – he has already solved the problems and can see a completed building in his head.''

Possibly the most damaging of all the misinformation spread about Utzon, this rumour first appeared in a calculated way before his departure, in order to precipitate it. After this departure it was repeated in order to justify his removal, and it has been perpetuated ever since.

By the time Utzon left Australia in 1966, the vast concrete shells of the exterior were virtually finished, but they were open-ended structures with no interiors and none of the glass walls that would enclose each end of each shell. Utzon's scheme for these walls was based on the subtle unfurling of the wing of a bird. Each piece of glass was to be housed in plywood mullions, each would be prefabricated and then put together on-site, and there were to be a minimal number of different shapes and sizes of glass.

Peter Hall, the architect brought in to replace Utzon, took a completely different approach. His glass walls, rather than draping down like a curtain, jutted out almost horizontally. Little of the nuanced and delicate effect of Utzon's ideas remained; his guiding philosophy of additive architecture was nowhere to be seen on the inside of the building. Hall proudly boasted that every one of the hundreds of pieces of glass in his walls had to be cut to a unique shape and size, all determined by a computer program – and as a result enormously expensive and time-consuming.

Utzon claimed that, had he remained in Australia, he would have finished the building within 18 months. He had already worked on the project for nine years, solving the most difficult of problems – how to build the shells. It seems hard to believe that the interiors, no less important but far less demanding, would have taken him almost as long again, which was what they took.

It's important to remember that for the first three of those nine years, no building work had begun. In addition, when he left the project many of his ideas for the interiors were well in hand, drawings existed, and some models had already been built and tested by plywood manufacturer Ralph Symonds (although this was done at Symonds' expense and did not come close to the volume of work needed for Utzon to fully test his ideas).

The new architectural team began on the interiors from scratch, since Hall, after taking inspiration from Utzon, developed his own quite different approach.

The six years of building work under Utzon cost $22m. The new team worked for nearly eight more years and spent a staggering $80m. If Utzon had continued in the job, spending at the same rate and finishing in the timeframe he gave, the total cost would have been $52m instead of the actual $102m. Robert Askin, the premier of New South Wales from 1965, had complained bitterly about the cost of the project while in opposition, and then once in government spent at a rate conservatively estimated to be 96% more than the previous government.

The truth is there was no ''mess'' at the Sydney Opera House under Utzon. There had been many problems, that is true, but in every case they had been solved with original and exciting architectural ideas. There was no reason why Utzon's successful approach could not have continued to completion. The Australian architectural profession was united on this point, almost to a man (there were few women; as late as 2004 only 1% of directors of Australian architecture firms were women). Even Peter Hall himself had been one of the first to sign the petition calling for Utzon's reinstatement – but that was before he decided to accept the job as his replacement.

The fact that in the end, the interiors and the glass walls that enclose the shells were vastly inferior to the magnificence of Utzon's plans for them was due not only to Hall being unable to match Utzon's design brilliance, but also to changes demanded by the government in the seating and basic functions of each hall. It's this that gave rise to the standing joke, ''Australia has the best opera house in the world – the exterior is in Sydney and the interior is in Melbourne.''

One of the most damaging acts of the government and the Opera House Committee after Utzon's departure was to dramatically change the brief he had been given. The major hall, which under the original brief was to be dual-purpose, both a concert hall for symphony orchestra and an opera theatre, was changed to accommodate only the former. At the same time the number of seats in it were increased.

Opera was shunted off to the minor hall, which was originally intended for drama only, because in the mid-1960s fewer people in Sydney attended the opera than attended symphony orchestra performances. Even though it was an opera house that was being built on Bennelong Point, the government decided, with no forward thinking at all, to put greater emphasis on the concert hall, to the detriment of opera. Askin, Hughes and Opera House Committee heavyweight Sir Charles Moses, the revered head of the ABC, could not imagine a time, less than a decade later, when audiences would come in numbers to the greatest opera house in the world to see – opera.

The problems with the interiors of the Sydney Opera House, which derive from the government's changed brief and the new architect's inability to deal with it, are so grave and numerous that it is impossible to list them here. It is enough to say that no grand opera, such as Verdi's Aida, can be properly staged in the concert hall (the major hall) because it has no staging gear. Nor can such operas be staged in the opera theatre itself (the minor hall), because it's too small.

In a tragic metaphor for where the whole project ended up, the staging gear, brought at massive expense from Austria, was removed after Utzon's departure and sent to Long Bay Prison for inmates to cut up as scrap metal. Utzon told me that the demolition expert who removed the gear was distraught, saying ''it was like cutting up a live deer''. Moreover the minor hall can only accommodate ballet by putting the dancers at risk. Performers are forced to run off into wings that barely exist, and as a result injuries have been common. The inadequate dimensions of the orchestra pit have led to musicians suffering hearing loss and have severely compromised the acoustics of the hall.

The acoustics of the major hall are also inferior, despite many ad hoc fix-ups, including, early on, the installation of 18 huge acrylic ceiling rings designed to reflect sound back onto the stage so that the orchestra can hear itself perform. It has been a sad and fruitless effort to improve the delivery of the one thing the project was meant to be all about – fine music.

There is one final nail in the coffin of the idea that Jørn Utzon did not know how to finish the Sydney Opera House and so resigned: the Kuwait National Assembly Building. Utzon designed this monumental work after once more winning an international competition in 1971.

Anyone who has seen its massive curved concrete forms, reminiscent of Le Corbusier's famous High Court Building in Chandigarh, India, immediately recognises it as no less impressive and certainly no less complex than the Sydney Opera House itself. Building work began on it in 1978 and was finished in 1982, and the whole building conformed to Utzon's philosophy of additive architecture.

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