What's Cookin!
In Breath of the Wild, it is encouraged that you cook meals and elixirs with the ingredients you farm while on your adventure. However, I think that this counts as a secondary system because you can survive by eating the raw ingredients. This may give you lower health restored, but the game is still playable for users that don’t cook.
GIDDY UP!
Link also has the ability to mount on horses and tame them to speed up the journey. I count this as a secondary system because the player can still get around the land on foot, but it would just take them a bit longer. Horses are also found in specific parts of the map so the user is already getting around on foot more than riding horses.
If cooking wasn't an option in the game, its not game over; however, it would just make playing much harder. You would have to farm more since you’d be consuming your raw ingredients to restore your health. It would make fighting enemies more challenging because, as you progress through the game, the level of difficulty of monsters goes up.
This also would turn achievement and creative based players away from the game. Those that cook usually like to experiment new recipes and have a sense of fulfillment when they make something new for the first time.
On the other hand, not much would change if the player didn’t have the option to ride horses. Since for most of the game players are already getting around by foot, having a horse would just aid the player to get places faster.
However, users that play for immersion and mastery would think this is a system that belongs in the game. They strive for the rewarding feeling of being able to master riding a difficult horse and using them to battle enemies. It also may be immersive for those that have never ridden a horse to get a sense of how it’s like by playing.
Although Breath of the Wild has a crafting system for food and elixirs, I would want them to also have one for weapons. I think the gameplay would motivate users to explore more of the map to find rare items they can use to build weapons. I also think this would attract more players that are achievement and creative based since they can now experiment with making new weapons.