It is surprising only when you are not aware of the right definition of energy.
The energy is a ratio between "action" and time, where "action" is a primitive quantity that does not depend on the system of coordinates.
While energy can be computed with various other formulae, like the product of force by length, all the other formulae obscure the meaning of energy, because they contain non-primitive quantities that depend themselves on time and length.
So energy depends directly on time, thus the properties of time transfer to properties of energy.
Similarly, the momentum is a ratio between "action" and length, so the symmetry properties of space transfer to properties of momentum, resulting in its conservation.
The same for the angular momentum, which is a ratio between "action" and phase (plane angle of rotation).
The energy is a ratio between "action" and time, where "action" is a primitive quantity that does not depend on the system of coordinates.
While energy can be computed with various other formulae, like the product of force by length, all the other formulae obscure the meaning of energy, because they contain non-primitive quantities that depend themselves on time and length.
So energy depends directly on time, thus the properties of time transfer to properties of energy.
Similarly, the momentum is a ratio between "action" and length, so the symmetry properties of space transfer to properties of momentum, resulting in its conservation.
The same for the angular momentum, which is a ratio between "action" and phase (plane angle of rotation).