"Wasn't it 'Beyond the Fringe' (Peter Cooke, Dudley Moore, Jonathan Miller, and Alan Bennett) that saw the re-emergence of satire and didn't Frost just jump on their coattails?"
Yes, absolutely! TW3, which lasted for just over one year, was a ground-breaking show in many ways, and David Frost was its presenter. As such, he was the "face" of the show and many people thought he wrote the whole thing. But he didn't. He was "just" the presenter. The show was devised, produced and directed by Ned Sherrin. It had many writers - the "usual suspects" plus some who might surprise you such as John Betjeman, Roald Dahl and Gerald Kaufman. But not David Frost.
The Nixon interviews, however, were a stunning piece of TV journalism, unparalleled IMO. They don't warrant his memorial stone in Westminster Abbey, though.