if a specific variable does not have a discernible impact on the resulting value, it is irrelevant to the equation. Such a variable may exist merely as a conceptual "comfort" to the human method of perceiving the universe, but that doesn't mean it serves any meaningful/rational purpose within the equation.

The variable may be meaningful but redundant. A database programmer would say that you don't have to keep a value in a column of the table, if you can calculate it from the other columns.

If all possibilities exist at all times as variable probabilities

Amplitudes, not probabilities. They are complex numbers, which is why they do the weird quantum things, such as two nonzero numbers making a zero sum. -- If you have 5% chance to win a lottery A, and 5% chance to win a lottery B, you cannot as a result have 0% probability to win either A or B. But a photon can have 5% chance to hit you if it goes through slit A, 5% chance if it goes through slit B, and 0% chance if both slits are open, if the amplitudes happen to be antiparallel.

What we see as probabilities, that's just a ratio between the squares of the absolute values of the amplitudes. (I don't fully understand why, so I can't tell you more about this.) On large scales those amplitudes give results consistent with our knowledge of probability, which is somehow related to the mathematical fact that if you take two complex numbers a and b, then |a|^2 + |b|^2 on average equals |a+b|^2 (the equation is true when vectors a and b are perpendicular to each other).