Among family, I have found radically different approaches to reheating food that has already been fully cooked. Some will not eat last night's leftovers unless they have been microwaved to the point where every single part of the food is piping hot. Said people consider food that is "cold in the middle" dangerous. Others are happy as long the the meal is sufficiently warmed for it to be safe to eat.
This gives me my question. Why do leftovers need to be reheated before they can be eaten? Is it just for pleasure or is there an actual safety benefit?
The primary reason for reheating is just that warm food is more pleasant to eat. How warm, that is a personal preference - and stirring or heating longer can ensure more throughout heating.
Reheating does weaken and kill pathogens. However, properly stored food should not have a dangerous amount of pathogens to start with. And some pathogens can either tolerate high temperatures or excrete toxins that are not destroyed by heat. Thus reheating food that already has a high amount of pathogens is only partially effective. Heating before cold storage is much more effective, as the pathogens do not get the chance to grow in the first place.
You don't. Reheating food does not improve food safety, it is purely a matter of taste. Even "piping hot" is not hot enough to kill off any pathogens. If it's safe to eat warm, it's safe to eat cold. As an anecdote, my sister considers last night's leftovers, cold directly from the fridge, the most delicious of breakfasts. Regardless of if it's pizza, a curry, or a beef stew.
We don't need to reheat food. Cooked food can be eaten cold. We may want to reheat food if its something that would be easier to eat or tastes better hot; or to kill bacteria if its been sitting out at room temperature and may pose a food safety issue.