Is “want” a causative verb?

I’ve always held on to the definition that Causative Verbs express how the Noun before the Verb influences the execution of an action.

Similarly, the Longman Student Grammar of Spoken and Written English defines them as:

“Causative Verbs… indicate that some person or thing helps to bring
about a new state of affairs.”

I know that the verbs have, get, make, and let are the four prototypical Causatives. But then I got to thinking that let doesn’t really “make” anything happen. And I just bunch let up with the other three (also allow) because of their similar structures and because it’s more convenient to teach them as a group.

When learners and teachers expand the definition beyond the four most common Causatives, in both active and passive-like structures, the lines can get blurry. There are many long lists on the Net (one listed as many as 90 and called them “mostly Causatives”). I guess the problem is the definition of what’s Causative to begin with. There are also those people who would identify Causatives by certain patterns that the words follow.

In any case, for this particular question, I’d settle for one verb that I’ve seen making the rounds on Causative lists: Is want a causative verb or not? And for me to make a sharper delineation of what’s causative, I’d have to ask why.