Yes, but, again, this is only because you have imperfect information about the underlying physical system. The array of possibilities presented by classical statistics are strictly epistemic; the actual real state of the system you're analyzing is always definitive and determinate.

You are glossing over my point. I’ll try to put it as concretely as I can think of:

Assume for the sake of argument that there is a process in an otherwise classical physical system that is truly nondeterministic, meaning there is randomness that isn’t due to any hidden variable or otherwise incomplete knowledge of the state of the system.

When describing such a system, you will run into the same dilemma of either needing a “wavefunction collapse” or “many worlds” interpretation of your statistics.

And yet this model is not quantum. It is a classical nondeterministic model.

My point being, it’s the existence of true nondeterminism that leads to the “many worlds” idea, not the other strange properties of quantum mechanics.

If you can demonstrate that quantum mechanics is just a different statistical model of classical physics, it would be a revolution in science.

I really, genuinely, think this is not a controversial take. The idea that quantum mechanics is more of a rethinking of statistics than physics comes from my own personal experience studying quantum physics. Most of the time, you take the classical Newtonian mechanics equations (sometimes including “corrections” for relativity), and treat them with the “quantum mechanics” version of statistics, and out pops all the important things you’d like to model, like how electrons arrange into orbitals in an atom. The results of slit/entanglement/bell experiments depend on having an object that obeys quantum statistics, but it can be a wide variety of objects with vastly different physical properties and behaviors (e.g. slit experiments have been done with both photons and electrons).

The important part isn't just that these states are possible, it's that they have real physical existence.

I don’t think there is any reason to believe the “other worlds” needed to analyze quantum systems “physically exist” to any meaningful extent. It’s the same as considering all possible outcomes of a classical truly random event (if you assume there exists true nondeterminism, not simply a lack of complete information).