Of course, a multibillion dollar pension fund does not want to directly write John Doe a mortgage and deal with him. Their business is giving money to pensioners, not selling mortgages. They would rather buy a bundle of thousands of mortgages at once and outsource the hassle of taking the payments to someone else.
The bundling and administration of mortgages is akin to a manufacturing process for electronic flow meters. The customer just cares about seeing a number go up, and pension funds just want to see money hit their accounts.
Since a great way of turning a bunch of cash upfront into a larger amount of cash over decades is through mortgages, banks unfortunately have to find actual people and help them buy a house.