And nor is Simon's output all about laughs.
"The comedy writing reputation is from the beginning of my career," says Simon, speaking from his New York apartment. "But apart from the first couple of plays, I don't sit down and say I'm going to write a comedy. I sit down to write a play."
But for all that, it is fair to say that Simon has taken to the limit the maxim "write what you know". He writes about himself and the people around him, including his wives. His first, Joan Baim, with whom he had two daughters, died of cancer in 1973, a trauma that led to Chapter Two, a play about emergence from grief and falling in love again. Simon's second wife Marsha Mason starred opposite Richard Dreyfuss in The Goodbye Girl (for which Dreyfuss won an Oscar), and nine years ago Simon married for the fifth time to his fourth wife Elaine Joyce. The extra wedding is because he married his third wife, Diane Lander, twice.
Simon will not be travelling to London for the opening of Sweet Charity. His health is less than tip top, and he is busy reworking the book he wrote for the musical Promises, Promises, based on the Billy Wilder film The Apartment. Promises, Promises opens in New York just before Sweet Charity opens in London. It must feel like old times for the writer once known as the King of Broadway. But it is not.
Last year a tremor shook up New York's theatre landscape when one of Simon's most bankable plays, Brighton Beach Memoirs, closed soon after it opened.
"Things are changing," says Simon who puts the failure down to more than one factor. "It was a terrible thing that happened. We closed the next day after the New York Times review. We were put in 41st Street. Broadway stops at 42nd street, so that was another reason we didn't do well. And we didn't have any stars. On Broadway, if you don't have stars, you're not going to get the people to come."
It was not always that way. Time was when there was no star name in the theatre bigger than Neil Simon's. In terms of popularity, he leaves Arthur Miller, Eugene O'Neill and Tennessee Williams in his wake.
The New York Times review was less than gushing, but it could be argued that is was part of a reassessment of Simon's work that questions the personality of the plays and asks if the Simonesque moral - "it doesn't matter how much pain you go through as long as you grow and learn by the experience" - has become dated.
Yet the best of the plays - Barefoot, Lost in Yonkers, which won him a Pulitzer, and what is known as the Eugene trilogy of Brighton Beach, Biloxi Blues and his third explicitly autobiographical work Broadway Bound - will always be constantly revived.
Simon has not a single chip on his shoulder about theatre critics. "I don't pay any attention to what people say. I write what I write. But you can't avoid critics. It's rare they're going to say that something is really great. And then you leave it up to the audience to have the final say. As for the critics who are out to kill you, I don't care about them. What are you going to say to them? 'Give me a break?'"
The big break came for Simon when he decided to escape the treadmill of writing TV comedy. He learned his trade writing material with his older brother and mentor Danny for stand-up comedians in the Catskills. Many of the performers were fading talents living on past glories. It was this world that Simon had in mind when he wrote The Sunshine Boys. The comedians he would soon be feeding lines to in TV were the kind of performers most comedy writers would give their writing hand to work for - Sid Caesar, Jerry Lewis, and Phil Silvers, the star of Sgt Bilko. For the three years the 19-year-old Simon worked on Caesar's Show of Shows he had to battle with bunch of fellow unknowns. One was called Mel Brooks, another Carl Reiner. For a year or so, the team was joined by Woody Allen.
"In the writers' room you fought for your life and your laughs," remembers Simon. "Sid Caesar would sit in the middle. He would come in the morning take his pants off and sit on a stool in his shorts. We would have to get his attention to be heard, only instead of raising your hands like schoolchildren we were screaming. I sat next to Carl Reiner because I knew I could talk to him and, through him, I could get my lines through. And Carl would say: 'Neil's got it, Neil's got it!' That's how I learned, and after a while it was time to move and start on a play." The play was Come Blow Your Horn which later got made into a movie with Frank Sinatra.
"It wasn't much of a play," says Simon, "But it gave me enough money to get through to the next one."
Does he see many of his colleagues from the old writer's room? "Only Carl Reiner when I get to California." Not Mel Brooks? There is pause. "The thing about Mel is that he would make you laugh more than anyone in the world. But he was also someone you wanted to kill more than anyone in the world," he says. It probably means no, not Mel Brooks.
There might be another reason why Simon is not coming to the opening of Sweet Charity. It was a project which the show's director/choreographer Bob Fosse brought to Simon. Fosse's script was tinder dry. He asked Simon to give it a lift with some humour, which he did brilliantly. But the book is still considered to be the show's weak point, and Simon himself has said that he never considered the script as his own.
In many ways, it is a series of great one-liners. And despite great one-liners being a signature of Simon's work it comes as a surprise to hear that he resists the association. "The comedy writing reputation is from the early plays," he says. "I'm not denigrating them. If the show is funny, it's funny."
But is it not great to be known as the king of the one-liner? "I don't like to think that that's me. These last 40 years I've written plays mostly. I don't even know what a one-liner is," he says.
And you can see what he means. Neil Simon fans sit down to Neil Simon plays and films and wait for Neil Simon lines. In the film of Sweet Charity starring Shirley MacLaine, they wait to see the lovelorn Charity sit in that nightclub full of celebrities, look around and say: "I'm the only one I never heard of". And they wait for one of her fellow dance hostesses to describe Charity perfectly as running "her heart like a hotel", with guys checking in and out. But the lines would mean nothing without a context - called plays. "I'm still working on plays," says Simon. "And I never think in terms of jokes. I hate jokes. Jokes are a ridiculous thing."
With Simon, playwriting is a process undertaken with pen and paper. There is no computer. Not even a typewriter, other than the one used by his assistant for typing up his long-hand. "I get an idea for a play and sometimes I don't know where it's going. I just go line by line or word by word. But then you see it. The people in the play, they're the ones who control it. And then suddenly it's not about showbiz, its about real life, at that stage.
"After I give it to someone to type, I read it and then I say: 'Okay, I have to make a lot of changes here. So I do it over, and over and over. Then I get to rehearsal and start making changes every day. It just goes on and on and on." And then after some thought, he adds
"But I'm slowly pulling away from it. I just write what I can every day. And when I get tired of it, I watch baseball."
