The food/strength/stamina system just makes you pay attention to what you eat and how you fight.

During a fight, you have to pay attention to stamina, creating time and space to take breathers. Making the other guy do the hard work was a vital skill for melee warriors irl. A lot of people died because they were too fatigued to defend themselves. Our protag even has a dream about dying that way.

After a while, managing stamina becomes part of your planning and tactics. Getting good at something is part of the fun of a game. Acquiring competence feels good.* "What is happiness, but the feeling that resistance is overcome…"

*(Edit) Thrift, thrift, Polonius "Getting good feels good."