Because I've defined them that way. I mean them to be independent choices you could make when designing your model that could be varied to fit the data. If two aspects of the model are not independent; i.e. they are covariant in some way, then there is some common parameter that explains them both, and that parameter is the one that should be seen as an input to the model.
> We can roll a die 100 times, 1000 times, 10K times [...] That's what we mean (if we're frequentists)
We're not frequentists.
You can't "re-roll" the 2016 election 10K times, either. There was only one, and there was only one way it could come out; we just didn't know enough to say what it would be before it happened. All the particles in all the voters were obeying the laws of physics at every moment; never was there any freedom for a different outcome. Nonetheless, even though there was/is only one "ground truth" that could ever be, we assigned probabilities to each possible outcome, given our incomplete knowledge.
This is a pretty standard application of probability. State estimators (e.g. the Kalman filter) are doing the same thing— you have some noisy readings of reality, and you use Bayesian logic on some assumed probability distributions to pick the estimate from the space of possible "ground truths" that has the highest probability of being the right one.
Concretely: I'm measuring roll rate, local acceleration, compass heading, barometric pressure, and GPS, all with significant error, and I want to know where my quadcopter is most likely to be at the current moment. There is only one true answer to that question, the quadcopter is in one place, not 10,000 places (or 10,000 flights), there is a single ground truth. But Bayes will give me a probability, given my readings, that any given estimate is the true ground truth (and some math will help me solve for the highest one).
In this case, instead of assigning probabilities to possible election outcomes or system state "ground truths", the "configuration space" is models of reality. But all we've changed is the domain of our probability distribution; the math doesn't care what kind of thing our "ground truth" represents. And it doesn't matter if reality contains only one "ground truth" or many; the fact is that we are choosing between many options (and we are ranking them by likelihood).