As a matter of fact, it sort of is. Look up Cede & Co and the Depository Trust Co.
"While private-company stock is still directly owned by shareholders, nearly all publicly traded equities and a majority of bonds are owned by a little-known partnership, Cede & Co., which is the nominee of the Depository Trust Co., a depository that holds securities for some 600 broker-dealers and banks. For each security, Cede & Co. owns a master certificate known as the "global security," which never leaves its vault. Transactions are recorded as debits and credits to DTC members' securities accounts, but the registered owner of the securities — Cede & Co. — remains the same.
What shareholders have rather than direct ownership, then, "is a [contractual] right against their broker...The broker then has a right against the depository institution where they have membership. Then the depository institution is beholden to the issuer. It's [at least] a three-step process before you get any rights to your stock." -American Banker, July 27, 2016 [0]