There are iconic architects and there is the architect who is the icon of iconic architecture. Whether he wanted to or not, Frank Gehry, as the creator of the titanium-clad Bilbao Guggenheim, made the original for 10,000 wannabes – pointy, swooshy, shiny things, would-be masterpieces that proclaimed regeneration for whichever ex-industrial swamp or intended megalopolis that happened to host them. He was feted in magazines and film and by an appearance on The Simpsons. He became the epitome of the idea – again, without much reference to his own wishes – that genius in architecture lies in spectacular shape-making.

Then there was the inevitable reaction. Iconic architecture came to be seen as wasteful, extravagant, unsustainable and, worse, a gaudy distraction from the dark financial forces for which it was a bauble. It seemed perfectly to encapsulate the great pre-crash deception, by offering only the appearance of glamour and prosperity. According to the art critic Hal Foster, Gehry's Walt Disney concert hall in Los Angeles is a "media logo" and his style of architecture is a "winning formula" for "any corporate entity that desires to be perceived, through an instant icon, as a global player". Someone started selling T-shirts saying "Fuck Frank Gehry" (and he bought some).

Not that he or his office seem unduly perturbed by the change in the critical wind. Recently his Signature theatre in New York opened, one of several projects in a city that once shunned him. Last year he completed the New World Symphony, a complex of performance and rehearsal spaces, in Miami. He finished his first skyscraper, in Spruce Street, Lower Manhattan.

Meanwhile, he is embroiled in a different controversy, with attacks coming from a more conservative direction than Hal Foster's: his proposed Eisenhower Memorial in Washington DC has drawn the ire of some of the president/general's relatives. They don't like it that Gehry wants to show Eisenhower as a "barefoot boy" from Kansas, rather than in the full pomp of his adult success.

"There is a backlash," says Gehry, now aged 82, "against me and everyone who has done buildings that have movement and feeling", that is "self-righteous" and "annoying… The notion is that it is counterproductive to social responsibility and sustainability. Therefore, curving the wall or doing something so-called wilful is wrong and so there is a tendency back to bland."

Frank Gehry: ‘My buildings are all on budget.’ Photograph: Torsten Blackwood/AFP/Getty Images

He argues that what he calls "expression" is essential. "Most of our cities built since the war are bland," he says. "They're modernist, they're cold, and now architects want to go back to that. But there are people in the community who want a little more juice, something to relate to, and so they seek out artists and the artists they seek out have become very wealthy and they have big studios." He mentions Olafur Eliasson and Anish Kapoor: "They have big operations going; they have the money, they have the know-how, they have the talent to build big structures."

Artists, in other words, are commissioned to build public structures because they address needs that architects don't satisfy. "You can't dismiss it as a force," says Gehry. "If there's a void they'll fill it." He does not have a problem with artists taking this role either – "hopefully it is collaborative" as in projects he used to do when he and Claes Oldenburg "played together" – but "the architects won't go there because they're being told not to. 'Don't be a naughty boy now.' You know what I mean?"

Nor does expression have to be extravagant. "My buildings are all on budget," he says, and he is proud of his practice's methods: "We have one hell of a delivery system." The Spruce Street tower has a surface of rippling stainless steel that looks expensive but which, he says, costs no more than a standard curtain wall. This was achieved by working with the manufacturer, testing options again and again so that waste and the cost of changing mistakes, which often account for a large proportion of construction budgets, were eliminated. The ripples also look like gratuitous decoration, but Gehry says they are purposeful: "They are just bay windows; they are maybe 10% decorative."

He has set up a company, Gehry Technologies, to sell his expertise in computer modelling to other architects. He also uses the inventions of others such as iCrete, or "intelligent concrete", a version of this sloppy, messy building material that is computer–calculated to achieve the ideal specification, which saves on waste, which saves money and reduces carbon emissions. He scoffs at the idea that his architecture is unsustainable: "We've been involved in environmental issues for 40 years."

If he is keen to rebut the notion that he is a self-indulgent artist, this is possibly because his parents thought he was. "When I was a kid, my father didn't really have much hope for me. He thought I was a dreamer; he didn't think I would amount to anything. My mother also. You know all parents do that with their kids, but at that time they expressed their worries more than we do now." Building in New York gives him satisfaction "because my father was there as a kid and he never really experienced me as an architect".

Other planks of the Gehry defence include the fact that, pre-Bilbao, his architecture was not about titanium monuments, but making the most of humble materials, such as plywood and the chain-link fencing that is much used in his adopted home town of Los Angeles. He was engaged, and earthy, and concerned with the undervalued and the overlooked. He does not see his business as flying into cities and dumping masterpieces on them, but believes that his works respond to the places they are in.

He does not always feel the need to employ his famous curves – "I can do square too." The Signature theatre is mostly about interiors and the "interaction between actors and audience" that is "palpable" and "magical"; it's also about giving its three auditoriums a separate but linked identity. Accessibility is one of the theatre company's aims and his spaces have a directness and a lack of flash that suit a venue with a maximum ticket price of $25.

He challenges, too, the claim that Bilbao is hostile to art, that it is too concerned with its own splendour to be a setting for the works of others. "The rap on Bilbao is a bad rap, fabricated by museum directors. Cy Twombly stayed away because curators at Moma told him not to go there. When he finally saw it he called and said, 'This is the greatest.'" The museum, he says, "has classical galleries for artists that aren't alive, and exciting ones for those that can respond".

I buy the Gehry defence. He is, in a way that others called "iconic" are not, a proper architect, in as much as he is concerned with how buildings are constructed and the making of spaces and forms. He discusses, for example, the question of the corners of buildings – if you have "an open corner" with the walls of the building pulled away from each other, it is "seductive", because it gives more freedom to play with surfaces. On the other hand, such corners can weaken the form of a building and make it look more like a stage set and he is a touch offended when I suggest that sometimes a stage set is what he is trying to create. Such conversations are basic to the practice of architecture, but there are plenty of well-known architects with whom it would be impossible to hold one.

He is not only concerned with the finished form but the processes that get him there. He appreciates his medium, but he is also aware of life beyond it. He is proud of the fact that a new book on management – Managing as Designing by Richard Boland and Fred Collopy – takes his design practices, which are iterative, based on testing and retesting ideas, as a model for other kinds of business. He also spends a month a year working with the department of microbiology at Princeton University, to see if his methods can challenge what he sees as expressive rigidity in cancer research. "There has been so much funding and so much science in big institutions in 30 years, but it hasn't moved the needle." This is a personal matter, as his daughter died of cancer, and he intends to continue this work for the rest of his life.

It is undeniable that his style and name have been exploited as logos. The Spruce Street tower is marketed "New York by Gehry", making both city and architect into a commercial brand. I am sceptical about his Guggenheim planned for Saadiyat Island in Abu Dhabi. It will be twice the size of the one in Bilbao, for no obvious reason other than that there is the money and space to do so, and where the Basque version has lively rapport with its complex urban surroundings, the newer one risks being a grandiose bellow into nothingness.

Perhaps Gehry could have resisted more the game of signatures and brands that goes with "iconic" architecture, but he is very far from the worst offender, and it is not the case that his buildings are pure shape, with no thought of what might happen inside and out. He holds on to the idea that architecture is about relationships, as between actors and audience in the Signature theatre, and between the people who make them and the people that use them. And, when his approach really works, the results are breathtaking. The Spruce Street tower may be a block of flats for the well-off, but it brings an energy to the skyline from which the whole of New York benefits.