Explicit hierarchy is useful to break ties. Not all questions have a universally compelling answer. There are often two or more competing "explanations" that are all sensible. Having nobody with the authority to make the final call often leads to uncertainty and endless bikeshedding.

In which case I expect the other person to agree that both options are equally valid and it's appropriate to choose randomly.

I think randomness is often underappreciated in business decisions. It helps create a baseline for performance measurement.

And I expect to have an experienced person in authority make the decision based on their "intuition", which just means the part of their accumulated experience that is difficult to formulate into an externally compelling argument.

This is actually a pretty good example of the phenomenon - if you and I were on a team and trying to figure out how to make decisions for our team, we would have this strong disagreement about whether it's better to break ties through intuition of randomness. My intuition is that intuition is better, and your intuition is that randomness is better. It's unlikely I can convince you that I'm right, or vice versa, so how should we break that tie?