It comes down to a couple of reasons, for convenience and well, other:
Copper is often used in roofing, both being an economical long term solution and looking good. It's also very malleable and easily shaped for domes and curves.
When properly designed and installed, a copper roof provides an
economical, long-term roofing solution. Tests on European copper roofs
from the 18th century showed that, in theory, copper roofs can last
one thousand years
Then why green? From the introduction of that article:
Copper’s most famous trait is its display from a bright metallic
colour to iridescent brown to near black and finally to a greenish
verdigris patina. Architects describe the array of browns as russet,
chocolate, plum, mahogany, and ebony. The metal’s distinctive
green patina has long been coveted by architects and designers.
This suggests that it's a building convenience, cost-saving, and trendy measure, copied and shared between architects and builders throughout Europe.
One final coincidence is that 2 Kings 19:26 mentions 'the grass on the housetops', and perhaps it's a pleasant coincidence to have a green-topped building.