There is another slant to this question to which I'm prompted by the memory
of (another ) Nat. Geographic article of many years ago. It included a
picture of the US base at the South Pole with a set of markers pushed into
the snow which traced the actual position of the pole over a period. That
is, the pole doesn't stay put but wanders over an area of some considerable
number of square metres. Thus for someone to say that they have reached the
pole is a matter of precision at the level of metres as well as kilometres.
If we say that the pole is a geometric point which can be straddled by a
person, it is capable of being reached but one wonders how many people have
truly satisfied that condition.