[throwaway2037]

We might be talking past each other, but this part:

    > Retail banks actually don’t ‘pool people’s money and invest it’

In all highly developed nations (G7 or OECD), most commercial banks invest a portion of deposits into government bonds and highly rated corporate bonds. They may also deposit funds with the central bank, usually called "The Window", but the interest rate will be (usually) lower than gov't bonds or corporate bonds. The difference between the interest paid on these deposits and earnings from these investments is called the NIM -- net interest margin. (This margin also includes lending these deposits at a much higher rate of interest than they pay depositors.)

However, the phrase "invest it" makes it sounds like they are gambling the money on speculative investments! There are very strict rules about what securities (classes and ratings) are allowed as investments.