My cat has never slept by my feet except when I am in my bed when he tends to sleep towards the end of the bed and therefore near my feet. In fact you’ll find that there are few photos of cats sleeping at a person’s feet on the internet except when in bed. There are more photos of cats sleeping near or on their caretaker’s head! Let’s remind ourselves that cats are individuals so when we ask a question like the one in the title we are bundling all domestic cats together which is incorrect. There may be a tendency for cats to do something but there will be exceptions sometimes.
However, some domestic cats must sleep by the feet of their owner because the question is posed to Google search. There are two obvious reasons (a) cats like to be near and in contact with their owner and (b) our feet smell and for cats scent is very important. It is a confirmation that they are near us which makes them feel more secure.
A position near our feet also allows a little distance or space between them and our heads. Often but not always cats don’t like to be close to our heads. It seems to unnerve some cats. Cats want to be close to us (if the relationship is good) and at the same time allow for some personal space.
Those are the readily apparent reasons why cats like sleeping by our feet. However, I don’t believe that this happens a lot except in bed as mentioned. If a cat wants to be close to use when out of bed he/she will sit on our lap or lie next to us if we are sitting down. They might lie on our legs when we are stretched out.
Warmth is a final reason. These are the driving factors for a cat: scent, warmth, contact.