I try to keep a few around because they are fun to watch. But will eliminate them if they get too plentiful. Never had any problems except for the one that got in my shed at my house. He made a big mess.If we’re talking the same rodent, around here we call them pine squirrels. They are one of the most destructive critters I’ve ever seen. Most people around here try to eradicate any they see.
There’s a raptor (I think a goshawk) nest no more than 25 yards into the trees above my yard. I have very few critters around thanks to them.