I can't tell you why NASA funded it or on the basis of what calculations, only that they did. Large bureaucracies frequently do things that look irrational from the outside, as do those looking to prevent or win geopolitical conflicts (including possibly negotiations involving the cost of operating the Easter Island runway you mention, negotiations that might have been significantly advanced by being able to say "we have an alternate landing site under construction").
NASA does lots of stuff in lots of places, so maybe they spent some money on a South Pole airfield. The only thing I can tell you for sure is that it had no connection to the Space Shuttle.
