I agree with you, except that "transitive" and "intransitive" are too general to be of much use.
Every verb in English (and I think in most languages) has one or more subcategorisation frames, which specify both the number and the kinds of the arguments it takes.
So follow usually takes a direct object (as you say, it is transitive).
Comply cannot take a direct object, but usually requires a "with" phrase: as you say, it is intransitive, but it is part of the syntax of this word that it requires a "with" phrase rather than, say a "to" phrase, so "intransitive" does not capture all the information.
For another similar pair, consider "eat" and "dine". "Eat" almost always requires an object (and if it doesn't, it is usually being used in the special meaning of "have a meal", not just "consume"). "Dine" usually does not take an object, and if it does, it requires an "on" phrase.
For further intricacies about subcategorisation, consider "want" and "wish". Both can take a clause as a direct object; but "wish" can take either a "that" clause ("I wish that I could fly") or an infinitive clause ("I wish to fly"), while in current English "want" can take only an infinitive clause ("I want to go home") and not a "that" clause (*"I want that I go/could go home"). Again, this is part of the intrinsic character of the particular verbs, but this difference is certainly not captured by "transitive" vs "intransitive".
As to why: like most "why" questions about language, the answer is "because that's how it is".
All of your examples are grammatically correct, so it's more a question of what sounds best, and what would be considered best style. Concerning style, there are a few general rules.
(1) If a direct object is a pronoun, then it is often preferable to express the indirect object with a prepositional phrase, placed after the direct object.
Consider the sentence, "I sent you it." Sounds awkward, doesn't it? It does at least to native speakers. This is likely due to cadence—the pronoun "it" doesn't like to be stressed. In cases like these, it's better to use the preposition. "I sent it to you." Now, that's better. However, I should add that there are exceptions to this rule. For example, "I sent you something" is a set phrase which sounds perfectly fine.
(2) Otherwise, if you wish to place the indirect object first, then you don't need the preposition.
If you place the indirect object before the direct object, then you may choose whether or not to use the preposition. It's usually best style not to use a preposition, as it normally sounds fine this way, and in general less is more. But if you choose to use the preposition, then it's still grammatically correct. It's more a question of style.
Best Answer
A prepositional phrase is a grammatical structure consisting of a preposition followed by a noun phrase. An adverbial complement is a grammatical function. Adverbial complements may be realized through prepositional phrases or other adverbials.
Consider:
I put the book down.
I put the book on the table.
I put the book down on the table.
There are verbs requiring complements without which the sentence they are part of would be malformed. In your example, the verb latch is such a verb. The addition of the adverbial particle onto in conjuction with the verb latch gives it an entirely different meaning than if latch were used in a sentence such as Make sure to latch the gate.
Therefore, I would argue that the verbal structure in your example is latch onto and that this structure is followed by the noun phrase a reason. In terms of function, I would say that latch onto is a verb and a reason is a direct object.