Is there an in universe explanation for why being unable to draw a card would make you lose (Rule 104.3c)? Running out of life, or losing as the result of a spell or effect, all make sense to me in universe, but I don't understand why a planeswalker running out of new spells would make them die.
Put simply, losing due to trying to draw from an empty library represents succumbing to madness.
In the flavor of Magic, the library basically represents memories and knowledge that you draw on to cast spells. In turn, mill effects are often represented as causing insanity or memory loss. For example, the first printing of the card for which "mill" is named, Millstone has this flavortext:
More than one mage has been driven insane by the sound of the millstone relentlessly grinding away.
Keep in mind that in general, mechanics are only loosely related to flavor, if at all. Not all mill cards are directly related to this flavor, but many have some relation to madness, or mental pain, or some other (generally unpleasant) interaction with the mind.