Ordinarily I would endorse Jacques' reasoning, but in the case of obviate, there's no need to rely on the brute fact that usage makes the rule, not the other way around. The ban on "obviate the need" was wrongheaded and shortlived, usage history reveals.
The OED online defines the verb as "To meet and dispose of; to circumvent, do away with, remove (a difficulty, need, etc.); to prevent or avoid by anticipatory measures." The grammarian Alexander Bain used the disputed phrase in "A Higher English Grammar" (1891): "Certain pronouns also, as will presently be seen, obviate the necessity of repeating the great substitutes of the Noun in composition."
But in the 1950s and '60s, says MWDEU, usage gurus Theodore Bernstein and Wilson Follett "seem to have invented the notion that obviate can mean only 'make unnecessary,' not 'anticipate and prevent.' They may have arrived at this conclusion by focusing too narrowly on the second part of the definition in Webster's Second [Unabridged Dictionary]."
I haven't (yet) found these authors specifically banning "obviate the need"; the accusation of redundancy must have been made explicit by later, lesser authorities. As recently as 2001, it is explained (and dismissed) in a usage note in Microsoft's Encarta College Dictionary:
Because one of the meanings of obviate is "to make unnecessary," it is sometimes argued that obviate the need (or necessity) for is redundant. An older but still current meaning, however, is "to avoid an anticipated difficulty." In a sentence like Addressing these issues early can obviate any need for a joint resolution, the need can be perceived as a difficulty -- or early consideration can make the resolution unnecessary, in which case any need for is indeed redundant. There is little reason to prefer either interpretation to the other.
And Garner's Modern American Usage (2009) demolishes the objection: "In the sense 'to make unnecessary,' obviate often appears correctly in the phrase obviate the necessity of or need for. These phrases are not redundancies, for the true sense of obviate the necessity is 'to prevent the necessity (from arising),' hence to make unnecessary."
One more peeve you can cross off your list, assuming you've ever had the misfortune to encounter it.