What is the real difference between direct objects and prepositional phrases?

I'm a fairly new ESL teacher. One of my students asked me recently why "...to comply with the rules of grammar" needs a preposition (with), whereas "...to follow the rules of grammar" doesn't. After some research, I decided that the answer is that "comply" is an intransitive verb, so it needs a prepositional phrase, and "follow" is a transitive verb, so it needs a direct object.

This is the answer I gave her, but I'm still unsatisfied with it. What is the difference, really? If "comply with" and "follow" are interchangeable in this sentence, why is one instance of "the rules" a direct object, and another a part of a prepositional phrase? Doesn't "with the rules" act as a direct object?

When a student asks me "why do some verbs need prepositions and others don't?" is the answer always "intransitive vs. transitive verbs?"

Thank you,

Lee