Oxygen can actually make a great electrophile! Obviously, oxygen is more electronegative, so an electron deficient oxygen is VERY unstable and reactive.
Many common oxidizing agents actually work like you've shown. For instance, bleach contains the O-Cl- ion, which can react a couple different ways including forming hypochlorous acid, which can then be nucleophilically attacked the exact same way as what you've shown, with chloride as a leaving group.
Nothing's special about carbon's ability to serve as a "frame" for good leaving groups, it's just that there are a lot of stable carbon compounds so we learn a lot of carbon electrophiles. Nitrogen and oxygen can react similarly; for instance, nitrogen chlorides are toxic because of their ability to react with nucleophiles in the body.