In general, phrasal verbs tend to be more informal than single-word verbs, so a reasonably good rule of thumb is to avoid them in writing unless you are writing something informal like a blog post. There are many phrasal verbs which are OK to use in formal writing, though. You should get a good sense of what is OK and what is not OK by reading content like magazines and newspapers.
An SAT essay is designed to test how well American students know "big" words (words used in books, etc.). For an American student, "give up" is an everyday word, while "capitulate" is a rare word that shows you are smart. (For an ESL student, "capitulate" might well be easier than "give up".) When a student writes the way they speak, using words like "kick out", the teacher assumes they have a poor vocabulary. Usually this assumption is correct. I know it does not have to be the case, but this is how it works in schools.