Aleatoric uncertainty is basically seeing randomness as a property of the universe, rather than a property of minds. Unless you verge into quantum territory, basically all randomness is actually epistemic uncertainty, and even if you verge into quantum territory, you can view quantum randomness as epistemic uncertainty.

Bayesians are comfortable viewing all uncertainties as epistemic. Non-Bayesians aren't, and all of the people I know who do professional decision-making under uncertainty dread someone even mentioning aleatoric uncertainty because it's a dead giveaway that the person mentioning it isn't Bayesian, and thus a long, unproductive philosophical discussion may be necessary before they can get anywhere.