The reason why cats sleep on their feet is because they can protect themselves. When living in the wild, cats often stand at high places and look out at their surroundings in order to detect potential dangers in time. Sleeping on their feet makes a similar sense, as it allows them to protect themselves and be able to react at any time.
Also, cats may sleep on their feet because they want to stay warm. Human bodies generate heat, so cats may feel warm while sleeping on their feet. Cats sometimes sleep on their feet because they like it. Cats are very independent animals who like their own space and choose where they sleep. If they find it comfortable to sleep on their feet, they are likely to do so regularly. Overall, cats may sleep standing on their feet for reasons of safety, warmth, or personal preference.