Consumables can be used as a push-your-luck or risk-reward mechanic. Does the player want to use them now? Or is it better to wait until later? in Foxwarrior example the player gets the consumables at a certain rate and don't want to use them any faster, because if they run out, the player could find themselves in a dire situation. That is a risk to be managed.

For another example, we could design the game with stretches where there is no access to some kinds of consumables, usually accompanied with closing the door behind the player. This will lead to three main behaviors:

 - The player would have to manage what they got carefully (do not use much more than needed).
 - If the player runs out or is running out of the consumable then the player will advance more slowly. This means the player will pay more attention to their situation and ways to get around without the consumable. This gets the player to try alternatives ways to progress and also increases the duration of the game.
 - On failure and retry, the player will probably look for ways to stock on large amounts of the consumable. The design could also leverage that to get the players to explore.

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Even though it is not what we usually think as a consumable, consider a shooter where the player can run out of bullet (not unheard of). Aside from the behaviors above (preserving bullets, aiming better - or perhap trick shots -, and looking for bullets), it will force the player to try other weapons. That helps ensure that all weapons have a chance to see play. Furthermore, in competitive game-play, trying to make the other player run out of ammo sometimes is a viable strategy.

  [1]: https://gamedev.stackexchange.com/a/171319/10408
  [2]: https://gamedev.stackexchange.com/a/171324/10408