I’ll add to what you said in your main comment and the one below that the $L^2$ norm is also the build-in norm of human beings (and arguably all animals), as we evaluate distances in $R^3$ in the Euclidean norm (of which the $L^2$ norm is a generalisation) rather than the $L^1$ or $L^\infty$ norms. The $L^2 norm also seems to be the norm of the physical world—Newton’s laws for example use the Euclidean norm.
I’ll add to what you said in your main comment and the one below that the $L^2$ norm is also the build-in norm of human beings (and arguably all animals), as we evaluate distances in $R^3$ in the Euclidean norm (of which the $L^2$ norm is a generalisation) rather than the $L^1$ or $L^\infty$ norms.
The $L^2 norm also seems to be the norm of the physical world—Newton’s laws for example use the Euclidean norm.