According to Quantum Field Theory, all 'particles' are oscillations in their own fields.
This is not true: According to QFT all space time is covered by fields represented by the free particle solutions of their corresponding quantum mechanical equation: Dirac for fermions, Klein Gordon for bosons and quantized Maxwell for photons. There is a field throughout spece-time for all particles in the table of the standard model of particle physics. Plain waves have oscillations but these are in a complex number space , not measurable in any way.
On these fields creation and annihilation operators propagate particles allowing for the possibility of writing Feynman diagrams to represent the integrals necessary in order to get measurable quantities: particles created and annihilated at the vertices of the diagram. These integrals predict measurable quantities for particle interactions and are validated by data up to now.
A free particle by itself cannot be represented by a plane wave, because free particles are localized in nature, see these single electron footprints. . To describe a single particle in the lab one needs a wave packet representation, i.e. a distribution of momenta so as to be able to get a mathematical model of a particle at a reasonable space-time location. Note that this means a given momentum with a spread commensurate with the Heisenberg uncertainty.
these fields have fluctuations in time and can never have 'zero' energy.
Energy has to be supplied in order to get measurable, observable effects from vacuum loops. All the listed "successes" inusing loop diagrams have energy supplied by incoming real particles.
Many physical effects attributed to zero-point energy have been experimentally verified, such as spontaneous emission, Casimir force, Lamb shift, magnetic moment of the electron and Delbrück scattering, these effects are usually called "radiative corrections".
Why don't we see random flashes of light in interstellar space because of the electromagnetic field getting enough energy to form a photon?
Getting energy from where? The photon field itself has no momentum it is just a "coordinate system" for an incoming particle with momentum. For an operator to operate on the field and create particles, energy must somehow be supplied. (For a real incoming from space photon the chosen answer here is relevant)
The handwaving discussions of vacuum loops independent of real particles is about cosmological models, where energy will be supplied by dark energy or something like that, but these are research models, not standard ones.