News that Sir David has decided to call it a day after the next election will inevitably lead to all the best broadcasters being linked to the job. Already we are told that Jeremy Paxman wants the Sunday-morning slot, though his more aggressive style may not be suited to the show.
It is a widely held belief that politicians prefer Frost because he gives them an easy time, but that's not altogether true. The so-called soft spot can often produce the biggest gaffes by lulling interviewees into a false sense of security. Tony Blair mistakenly blurted out Labour's big spending plans for health and education to Frost, months before the Chancellor's formal announcement.
Brown used to prepare more for Frost than the Today programme, and before every appearance, we would always make sure that at least one Sunday paper had an exclusive positive Brown story for the Chancellor to respond to. This ensured stories had legs for the Monday papers, and they would invariably run on all the Sunday news bulletins.
The editor of Frost, Barney Jones, who understands the importance of promoting his programme, always insists that an appearance with Frost is not followed with an interview elsewhere on the network - or indeed any other network. This forces all TV news outlets to use the Frost clip for their bulletins.
Jones can't enforce this, but if you ever want an invitation back to Frost, you would be very unwise to ignore this unwritten rule.
Frost also has the advantage of having the best contacts book in the business, so it's not only top British politicians who appear on his show.
Bill Clinton, George Bush, Richard Nixon and Nelson Mandela have done it. And footballers and film stars love to appear, too.
The question is whether the replacement show will have the same impact.
That does rather depend on who gets the job. Paxman and Jeremy Vine could both do well, but my tip is Andrew Marr, who has done such a good job as BBC political editor.
Whoever gets the gig should thrive, simply because the timing of the slot is so good - for politicians, journalists and spin doctors alike.