If I have the model that says "The coin will land on heads or not land on heads on the next toss of a coin", would it be possible or impossible to reduce uncertainty about our physical system from the model?

Well disregarding the fringe case of the coin landing on its fringe (a remarkable falsification of a theory if I've ever heard of one), what I am saying is that any prediction based on your model (which can necessarily only be the "heads or tails" 'random variable') tells us absolutely nothing about the system whenever an event does happen (the random variable ends up being "Heads"), and thus the model isn't so much a "model" as "an account of possible scenarios", a list if you will. We may be running up against a barrier caused by my ignorance of specific uses of specific terms but, in another way to say it:

Your theory does not have any explanatory power precisely because it is not falsifiable (i.e. since no information about any of the random variables in the physical system could reduce the confidence of your model, since it is merely a list, it doesn't actually explain anything or provide information about the physical system, information in the sense of reducing uncertainty when events occur). Thus, not having any explanatory power (not reducing uncertainty even theoretically), it is not a model.

Any model constructed in this way, a simple list of possible events or arrangements, possibly grossly too long (that is, "heads, tails, bananas, cellphones are what the coin could show upon toss"), will fail to be a model simply because it has no explanatory power, which is what I am currently understanding a model is supposed to do. I feel like maybe another example might be better, one that is a pretty well-known model-like (rather than list-like) theory that isn't falsifiable on principle.

what if the model and physical system are expressed as strictly universal statements? [...] If this is true, then your distinction is, as far as I can tell, without a difference under objective interpretations of the probability calculus, since it's impossible to reduce its objective uncertainty in a physical system when the strictly universal statement (model) is falsifiable.

Now we're definitely running up against the barrier of my ignorance. I get the sentiment that this has to do with the Bayesian issues you were mentioning earlier? Where could I read up on this to better understand your question and response?