Wikipedia says that
For technical reasons, the category $\mathbf{Ban_1}$ of Banach spaces and linear contractions is often equipped not with the "obvious" forgetful functor but the functor $U_1: \mathbf{Ban_1} \to \mathbf{Set}$ which maps a Banach space to its (closed) unit ball.
The category $\mathbf{Ban_1}$, in view of the above functor, is given as an example of a concretizable category.
What are these technical reasons? The choice of the functor seems quite odd and non-obvious. It would be great if someone could throw some light, please!