takes a very different aspect, depending on if you define it per volume unit or per radius unit
Just because the surface of a sphere increases with its radius, it increases the density per radius unit at a bigger radius as compared with the density per volume unit. The radius of maximum density is also larger if you use the density per radius unit.
For instance, the maximum density per volume unit is at the nucleus for s orbitals, while the density per radius unit is zero at the nucleus.
Same story with the Boltzmann distribution of momentum in a gas: the maximum per "volume" of k or p vector is around zero, while it's non-zero per unit of k or p "length".
Then, orbitals define an electrostatic and a kinetic energy, this latter increasing when the electron is more confined. s orbitals confine the electron only over the radius, other orbitals confine it around a plane or a direction, which increases the kinetic energy.