Why did greek designers take such great care when designing their buildings?
If the question is coming purely from a structural perspective,
the Ancient Greeks took care to build well in order to prevent the
building falling on top of them. If the question is coming from a
design perspective, e.g. the various columns and other design
elements, what is important to note is that most of the buildings
that we have from Ancient Greece and are popular attractions are
the major public buildings, like Theaters or Temples for the Gods
or Palaces and are naturally much prettier on those grounds (just
like how our theaters, centers of worship, and government buildings
are well designed).