I think such attempts are not widely disseminated / taught to young physicists because older / more experienced ones believe that quantum gravity will re-write the situation anyway. { QG itself seems necessary since in General Relativity you "solve for the metric aka solve for time" and that very same "time" is the background for QFT. So, we don't really understand this model element we call "time" - so elemental to all our ideas of dynamics - without QG. Of course, the most direct quantum gravitational phenomena are at, at present, a subtle experimental scales due to the size of 'G'. This need not remain the case -- once we know what to look for - e.g., https://en.wikipedia.org/wiki/Fraunhofer_lines were beginning to reveal atomic quantum physics a full century+ before Planck and barely after Benjamin Franklin-ian electrostatics and long before Maxwellian electrodynamics. }
I'm mostly just trying to strike a less hopeless note for jiggawatts and provide some reading material which might be accessible (if, as noted, probably necessarily preliminary).
The two theorems apply to logical systems which prove facts about the natural numbers. While this is an incredibly broad class of things, it doesn't include physical theories like quantum mechanics.
Quantum physics PhD here. It's because, we don't know. We don't have an ontology for quantum mechanics. We don't know what any of the mathematical model "actually is"
It's the same for basically all modern physics. We lack an ontology for it, so no we can't tell you "what it really is". Literally no one knows
But yes, the mathematical model is: a unit of excitation of the quantum field. What that actually is, is totally unknown