Not all of their entities are "not for profit". And some of them that are still raise eyebrows!
Blue Cross Blue Shield Association - Wikipedia
"While only some members retain nonprofit status, the ones that do have been criticized for holding excessive amounts of cash or excessive executive compensation. In 2014, BC/BS of Illinois (Health Care Service Corporation) was sued over its nonprofit status, with the lawsuit dismissed with prejudice and the ruling upheld on appeal.[25] Similar suits occurred with similar results in other states such as Oregon.[26]"