How is the rarity of cards in official preconstructed Commander decks determined?
You mention that each deck is a singleton deck, so each card is printed exactly as much as each other card within that product. This is true when considering just one deck, but if you look at multiple decks that are part of the same product (e.g. all of the C16 decks), cards at lower rarities are printed in more decks than cards at higher rarities. Common cards can be printed in 4 or 5 of the decks, while mythic rare cards are printed in only one of them.

Rarity also has some meaning other than the print run frequency in sealed products. In particular, the Magic Online format Pauper allows only cards that have been printed at common. Similarly, the unofficial format Peasant is similar, but has slightly less restrictive deckbuilding rules and allows some uncommons. So, we can assume that power level plays a role in determining the rarity at which a card should be printed.

In addition, Wizards' "New World Order" design philosophy, which has been in effect for several years, dictates that more complex cards should be printed at higher rarity levels. This is a less important consideration in decks of singletons, but it's likely that they continue to follow the same principles for consistency.