I think that sometimes people, especially people new to poetry, think of free verse as somehow less exacting, or requiring less effort. But what free-verse poets often learn is that just because the rules of structure and rhythm aren't predefined, doesn't mean that their words should be chosen less carefully. Ginsberg's Howl, like you mentioned, is written in free verse but the attention to phrasing, rhythm, word choice, reveal, arc, and theme are as meticulous as if he had needed to adhere to iambic pentameter.
So to answer your question, I'd say that structured poetry is an excellent way to practice expressing yourself clearly and fully while still constrained by rules of meter, rhyme, etc. But if your heart lies with free-verse, that's what you should write. Practice with one, write with the other.