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You're right that the dice are literally intended to represent a hidden variable. The difference between the frequentost and the Bayesian is that the frequentist only accounts for the hidden variable, whereas the Bayesian also accounts for the pre-test probability of the sun exploding. Since the probability of the sun exploding is 1 in a bazillion, multiplying that by 35 still gives you a very very low post-test probability that the sun has gone nova because 35 in a bazillion is still pretty unlikely

It is like running a casino versus gambling as an individual.

If I was running a casino and presiding over tens of thousands of bets daily, I would use frequency statistics to guarantee the house always wins.

If I was an individual gambler and determining my odds at a particular bet, I would use Bayesian.

It depends what the null hypothesis is here, but by construction, under a reasonable null, the p-value for an appropriate test would not be acceptable under a Frequentist framework.