The leader (down spout) is most lightly connected to a Strom line that over the years may have become blocked with leaves and other debris.
Personally I would try to have these lines either snaked or water jetted cleaned AND if that fails then relocate the discharge of the water.
The problem with just eliminating this down spout some codes are very strict about
1- Having storm water going on someone else’s property
2- Going on city property as this may over load the city catch basin capacity.
For every action there is a reaction think this one through.