On the substance of things, I think most cabinets do contain potential Presidents.
In the Obama administration, Tom Vilsack and John Kerry are both Presidential material, although their window closed years ago. But they could both govern if they had to.
Actually, all of his Secretaries of State are presidential material. Can’t remember offhand who the other one was, though.
Most SecStates are unless they were born outside the US.
I think Safire was speaking more prospectively - that is, every Cabinet should have at least one person whom you could imagine becoming President someday. Right now, that might include Thomas Perez (Labor), Julian Castro (HUD) and Anthony Foxx (Transportation). YMMV.
The last two Secretaries of State have been failed Presidential Candidate sitting Senators. The several before that, technocrats.
For the last few decade service in the Cabinet of the US has been for technocrats or politicians for whom further elective office has been out of reach.
Perez is too controversial, Castro can’t win statewide in Texas(winning statewide is generally a prerequisite to becoming President).
Foxx though, is definitely a prospect. But like Castro, he needs to win statewide office in NC. Given how bad the Democrats’ bench is in that state and how NC is fond of Senate turnover, Foxx could actually win a Senate seat there. Or perhaps run for governor.
Well before that, there’s been precedent for the office being a sort of consolation prize for unsuccessful presidential candidates (Henry Clay, William Seward).
Just one?!? That really is a difference then between the two systems. Usually I can see at least half a dozen on the front bench on the government side as potential PMs. And not just someday, but tomorrow, if the PM keels over.
They’re not on the front bench because someone handed it to them. They’re there because they’ve fought long and hard to get there, driven by ambition and ability.
And because they’ve demonstrated their abilities on the hustings, winning elections.
And because they’ve got the executive wherewithal to be trusted with a major department by the PM, who’s assessed them as being capable.
And the ability to hold their own in the debates and QP in the Commons, defending themselves and the government.
And (probably the most important) they’ve got the self-confidence and ambition to see themselves as PM.
They wouldn’t be on the front bench without all that.
Being an MP and a senior Cabinet minister is a grueling job.
The weak flame out or quit.
The strong jostle for position for the inevitable day when the Prime Minister retires or is defeated in an election, and someone new is needed.
Just by way of comparison, how many of the current Secretaries in Obama’s cabinet have held major elective office?
(Let’s define it as Senate, House of Representatives, Governor or other state-wide elective office.)
I know Kerry has, but I don’t know the composition of Cabinet well enough to hazard a guess for anyone else.
The current Obama Cabinet seems pretty unusual for having so few politicians. I think Vilsack, Castro (if you include Mayor of San Antonio as a “major political office”) and Kerry are the only three. (plus Biden, if you want to count the VP). The rest are technocrats/business leaders.
Foxx was previously mayor of Charlotte, N.C. (pop. 2.3 million in 2014), too. Otherwise you’re right.
Well, that is larger than several of our provinces, so your standard of a major electoral position may be a bit different from ours. 
Nobody seems to have noticed, but former IRS Commissioner (it’s not a Cabinet post, but close enough) Mark Everson is running for the GOP nomination on an… interesting platform. He’s a technocrat who talks like an old-school populist.
Well, Charlotte’s population is only 810,000, which I assume is still larger than several of your provinces. The mayor doesn’t have much say over the 'burbs.
Ah, yes, thanks. I had only seen the higher number for the metropolitan area, not the lower one for the population within city limits.