As it is known since 1900 (Lorentz et al) energy-momentum conservation
of the classical Maxwell field does not work in the case of point
charges and unbounded electromagnetic local fields.
QED is the first theory that turns energy-momentum conservation of
interacting bounded quantum mechanically charge distributions together
with their free radiation fields into a working principle.
And as we all know, this only works in the frame of a bit of fermionic
matter, relativistc an overall redefinition of nearly all observable
physical quantities by a renormalization procedure.