You're looking at it wrong. It isn't individual verbs that are causative, usually; it's the constructions they're in, which may or may not require them.
For instance, there's a causative construction with have
- He had his tires rotated.
meaning, in this case, that he caused someone else to rotate the tires on his car. That doesn't mean have is a causative verb; it's not. It just means the causative construction uses have.
The example sentences you gave (leaving off the irrelevant bells and whistles)
- People want their favorite words added.
- They want their issue done.
are both examples of the syntactic rule called to be-deletion. Note that to be may be added in each case, making a passive infinitive complement:
- People want their favorite words to be added.
- They want their issue to be done.
So that's what happened to those sentences. Want does not cause things, though it can motivate people to do things. But that's not causation.
The other two examples you mention are real causative constructions,
one with have that I mentioned above, and one with make, a true causative verb.