From the manga VB Rose: キャチ。In the manga, this phrase was used as an onomatopoeia to describe the sounds of being caught by someone after tripping. As far as I am aware, there is no phrase that accurately represents this idea in either kanji or hiragana. If you think about it, this sound does fit the situation. There is the sound of wind whistling through your ears as you fall (キャ), and then a light impact as someone catches you (チ). It is more pleasing to the eye (as well as simpler to add) in manga to see a short katakana onomatopoeia made of simple lines, than a longer hiragana phrase or a complex kanji character. It is also less distracting to a reader reading the English translation that has kept in the katakana than seeing a long phrase or complex character. Keiko had asked if I had perhaps missed a character, as she said the word キャッチ is usually used to imply catching something. But I double-checked the manga page, and the word was キャチ、not キャッチ。
From a McDonald's sign: ドライブスルー。This is a loan word/foreign word from the English "drivethru". Translating it into kanji or hiragana would mean creating a new word or character, and for something so close to the English equivalent it is much simpler to transcribe it phonetically using katakana instead. The Japanese did not have such a word before it was brought over from another country.
One of the textbooks mentioned specifically that katakana, "which has rather straight lines" is used for loan words and foreign names. I think they said it this way to make it easier to tell apart when looking at a piece of writing, as well as telling the reader they will at least know the type of word that is there, even if it's not something they can read/understand.
The second one introduces katakana as used for borrowed words and onomatopoeia. I find it interesting that they specifically mentioned the second one, as onomatopoeia are not something a new student will come across much as they are starting out, since they are neither very much in print (disregarding manga) nor very useful things to know for a new student.
The third source specifies that they are phonetic representations of sounds, which lets the student know that once they learn the basics, they will always be able to sound something out even if they're not sure what it means. Since they are phonetic though, most of the time the student should be able to figure it out.
The last textbook excerpt also mentions the difference in shape of the characters (more angular, as opposed "to the flowing lines of hiragana") and the fact that it is used for loan words, onomatopoeia, and also words the writer wishes to emphasize. This is the first time I've heard of the last reason, and I find it interesting. It also notes that younger people and people in urban centers are more likely to use katakana and loan words, even if a Japanese version of the word exists. I think this was partly to help reassure people thinking about visiting that if they get stuck, it will be easier to find someone who will understand at least part of what you are saying, especially if they are in an city and/or surrounded by younger people.