Is the Higgs field needed to explain the mass of the electron?

The self energy of the electron can be represented in two ways:

1. the energy required to bring a charge distribution from infinity to the size of the electron (assuming it is a point charge with no other structure)


2. the work required for the electron to move against its own electric field.

In the second instance, the action of accelerating the electron against its own field could define its mass (also assuming the problems of infinities are eliminated by the vacuum polarization at the quantum level). There does not need to be interaction with any other particles in that the action against its own field produces photons.

Why would a separate Higgs field be needed if the mass could be defined by the electron's own electric field?