There are way too many of these things. In the past I would have said "Who are we to say there are too many of any animal? Their population just responds to the environment, and they move into the niche, which man has made perfect for them." Which is true, but that was when I was young and didn't think humans had any business managing animal populations except to try to repair habitat and leave them alone. Gray squirrels, even in their natural native habitat have a strong tendency to become invasive and pesty. They rob songbirds of eggs and nestlings (which isn't really a problem most of the time, since those are usually the songbirds that do well in human-impacted places) chew holes in buildings, get into the trash, and cause lots of damage around the zoo.
Fortunately there is some predator pressure on them (red-tailed hawks mostly) but not enough. The next time we have a lean acorn year we are going to be up to our ears in starving squirrels, and it won't be nice to see.