I'm disappointed in the lack of imaginative responses to this question. I'm
sure the architects would find it much more interesting.
Someone wondered how could they get stuff up that high. Well, it could be
brought up in lifts, with cranes stationed every so many feet. Someone else
mentioned high water pressure. Well, it, too, could be pumped up in stages
and used in stages, so no "station or zone" would exceed reasonable design
parameters. Elevators would be a problem, but once again, in stages it could
be done. Total weight of the building would definitely be a problem. The
upper story swaying would demand attention. Heat loss and high maintenance
costs associated with constant weather and moisture would be a problem. Fires
might be catastrophic.
On the bright side, one would have good TV reception...