Eschewing trailing prepositions is a rule improperly inherited from Latin. It does not apply to Germanic tongues where prepositions are necessary to disambiguate verbs. For example, to ask about, to ask of, to ask to, and to ask in are very quite distinct. In Latin, the default position of the verb is the end of the sentence. Latin word order isn't fixed like English, so the ordering of words is a form of emphasis, and placing something in the final position, after the verb, is one of the strongest emphases possible. Putting a preposition in that position would be like someone screaming "WITH! WITH!" on a soapbox on the street corner.

It's a useful rule though: an English grammar book that proscribes trailing prepositions is one you needn't spend any more time with. Just put it down and forget that it exists.

Like so many other rules, it results from Latin-steeped scholars of the 19th century who were uncomfortable with the flexibility of their native tongue, and attempted to hem it round. It's understandable. These men knew they could use the full scope of expression of Latin. About the only person who's ever pushed English hard enough to make it creak was James Joyce.

Amusing aside: you can transform transitive verbs into nouns in English directly (to request, a request). You can't similarly transform intransitive verbs because they require a preposition. In German, you would say a for-ask or an of-ask, but we don't accept that in English. Verbs with both forms are an interesting grey area, such as to dig vs to dig for.