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You also have to understand the economics of a TV show. No show lasts forever and most popular shows are canceled not because the ratings drop significantly, but because after years of success, the actors/writers/producers make so much money that even a slight drop in ratings make the show unprofitable because the costs of producing the show.
Two and a half men only had a few seasons left anyway before it collapsed under it's own weight. So CBS swaps out Sheen with another actor and keeps going. Sure, people will say they won't watch but every TV show that changes a character keeps on going and the fans still tune in. So the show can very possibly be MORE profitable now that Sheen is out. Trust me, I am sure they did the calculations and came to the same conclusion.
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