You are glossing over my point.

I promise I'm not doing it deliberately.

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.

Yes, I would agree with that if we're using "wave function collapse" to refer to any truly probabilistic mechanism in a general sense (as, strictly speaking you could have a non-deterministic mechanics without wave functions at all).

But I note the important fact that you don't need both.

My point being, it’s the existence of true nondeterminism that leads to the “many worlds” idea

Well no, it's the existence of true non-determinism without any form of wave function collapse.

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.

Well if that's the case, with all due respect, I think you need to study quantum physics more. Because trying to overturn a century of scientific consensus is definitely controversial, at best.

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).

How, specifically, are you modeling the double slit experiment using only Newtonian Mechanics? How about quantum tunneling?

I don’t think there is any reason to believe the “other worlds” needed to analyze quantum systems “physically exist” to any meaningful extent.

Are claiming that super positions don't actually exist at all? Because, again, you'd better have a solid argument for such a radical claim.

It’s the same as considering all possible outcomes of a classical truly random event

Is it? Hard to say when we're talking about something that doesn't actually exist.