I think the obsession goes back further than Steve Waugh. Remember, Inverarity played alongside Doug Walters (The Man with the Golden Arm) who could also trundle down a few useful deliveries.
On one occasion, Chappell brought on Walters because a partnership was becomin irritating. Doug took a wicket in his first over, and was reported to have said, "Bloody beauty; 1 for none. What a great game this is. Did him with pace - lack of."
In recent years, the fetish with playing an all rounder picked up again when Flintoff carved us up in the 2005 ashes with 24 wickets and 400 runs. All of a sudden, every team had to have a Flintoff. And of course, Gilchrist changed the course of the game when every team had to pick a batsman that could keep a bit instead of a keeper that might be able to bat a bit.