In the Glass-Steagall sense, they probably shouldn't. Mixing commercial banking and investment banking was illegal from 1933-1999, and it is (arguably) one of the underlying factors in the 2008 financial crisis.
Note: There's a difference between being a custodian of customers' investments (brokerage / commercial banking) versus proactively investing customer deposits (investment banking).
Going to need a _huge_ source on that claim. Investing customer funds is the primary way banks make their money, and has been that way essentially since the invention of banking.
Note: There's a difference between being a custodian of customers' investments (brokerage / commercial banking) versus proactively investing customer deposits (investment banking).