Re: On the other hand....
"(eg incapable of telling that whatever 3547+2974 might be, it's not 4xxx or 5xxx)"
I think it has always been true that most of the population is incapable in that sense. :(
Kids today have separate maths tests where they are or aren't allowed to use calculators. In the ones where they aren't, they get tested on the kind of numeracy that you refer to. In the others, they get to show that they know what operations ought to be performed on larger calculations, without being held back by the tedium of performing them.
I'm a big fan of mental arithmetic and estimation skills, but I still think calculators are a good thing. In fact, I think the solution to the endemic innumeracy problem is to split "maths" into the elegant stuff and the practical stuff and let those who aren't keen on triangles and quadratics equations drop them and concentrate on areas and averages. (For similar reasons, I'd like kids to be able to drop English Lit and concentrate on the English Lang skills that might let them put a coherent document together, or understand one written by someone else. I do think that one of the more damaging tendencies in education in recent decades is ministers who think the solution is to broaden the core curriculum year on year until there's no room for the "lesser" subjects that might actually interest 80% of the teenage population. Yes it would be "nice" if everyone knew a little physics and biology, but it would also be "nice" if everyone knew how to read music and knew that there *were* such things as the rudiments of harmony even if they didn't understand them, had some idea of the last 500 years of European history, some idea of the artistic movements that had accompanied it, some idea of where it took place, and some idea of the religious certainties that had motivated almost everyone until at least 1800 and a whacking majority until very recently. The moon on a stick would be nice, too. But no. We have to study triangles and quadratic equations and Chaucer and poetry.)