Interesting idea, I approach the problem somewhat differently.
In my work, the deeper question is not simply what is mathematically admissible, but what can persist as a physically recoverable structure.
Not everything that is admissible must persist, and not everything that persists must remain recoverable.
That distinction becomes important when discussing negative probabilities, non unitary sectors, or exotic quantum states. As such a mathematical solution may exist within the formalism, yet fail to survive continuity constraints. Equally, a transient structure may exist physically while leaving no recoverable lineage.
As such, I view admissibility, persistence, and recoverability as three separate filters acting on reality. The structures we observe are those that successfully pass through all three.
That is where I would look for a resolution, rather than assuming every mathematically allowed state necessarily corresponds to a physically realised one.