Why does "want" catenate with a nominal plus to-infinitive whereas "insist" does not?

Question

Why can't you say:

"I insist you to do that!"

After all, you can say:

"I want you to do that!"

What's the difference between these two verbs, that they need to be used in sentences with different structures?

Answer 1

Insist is an intransitive verb. You can’t insist something or insist someone. You can only insist, and then say what it is you insist, using a clause beginning with that.

Want is a transitive verb. You can want something and even want someone. That’s why we can say I want you. That’s a complete sentence, but alone it means something rather intimate. That, however, isn’t the case when it’s followed by the plain form of the verb preceded by the particle to in your example.

Answer 2

There's no preposition in your grammatical sentence (the second one) – that's the infinitive-marker to (which looks exactly the same as the preposition to, though). I've edited the question accordingly.

If you look up catenative verbs (eg at Wiktionary), you will see the various ways different verbs catenate – some with an -ing form, some with a bare infinitive (like go in the US), some with a to-infinitive (like want, desire). Help accepts either a bare infinitive or a to-infinitive most of the time! Some verbs have different meanings with different forms of catenation, eg:

He forgot putting the light on.
He forgot to put the light on.

And, further to the cited article: some verbs give rise to catenations that can (eg want) or must (eg cause) include a direct object. This is called the complex catenative construction (mentioned in chapter 14 of CGEL):

I want to drive to London tomorrow.
I want John to drive to London tomorrow.
It caused John to have a sleepless night.

(Notice that the second to's in the first two of these sentences are indeed examples of the preposition)

However, insist doesn't catenate. What we have here is a reduced that-clause:

I insist (that) you do it.