If we are willing to understand the difference between an all rounder (Sobers, Miller, Faulkner, Botham, Imran, etc) and a "bits and pieces" player (Ronnie Irani and his superiors) that has been masquerading as an all rounder in some countries thanks to the proliferation of the limited overs format, and substitute the latter description in the thread-title, the motion is carried unopposed.
An all rounder is not produced by ignoring specialistaion and selecting a player in a team who is neither good enough to be selected as a batsman nor good enough to be selected as bowler. An all rounder is at least always good enough as a specialist in one area and often enough performs as well as a specialist in the other.
The so called all rounders that England and New Zealand, in particular, have produced by the dozens in the last decade or more are a joke compared to the rare group of talented cricketers who belong to this special club. To first include these apologies for all rounders in that list and then run down the place of an all rounder in the scheme of things is to completely turn logic on its head.