Tunneling is not owned by quantum mechanics.
A Newtonian point particle cannot cross a barrier with E<V. A wave can penetrate a forbidden region, decay exponentially, and re-emerge beyond a thin barrier. Classical waves do this routinely.
In frustrated total internal reflection, a classical electromagnetic field develops an evanescent component in a low-index gap. Put another medium close enough and energy couples across the gap. Waveguides below cutoff and acoustic systems exhibit the same mathematics.
The exponential itself is not a quantum fingerprint. It is a wave fingerprint.
What remains to reconstruct
An optical analogy does not automatically explain electron tunneling. A complete theory must derive the electron-specific dispersion, current–voltage law, state density, detector statistics and material dependence from its own ontology. That is the correct burden. The phrase “classically forbidden” only means forbidden to the specified classical particle model.
Interference has the same problem
Interference is ordinary classical wave behavior. What needs reconstruction in single-event experiments is not the fringe law alone but why localized detection events accumulate according to it. That directs attention toward source dynamics, persistent fields, detector thresholds and stochastic event formation instead of pretending the word “interference” has already selected an ontology.
Read a classical-wave tunneling treatment in frustrated total internal reflection.