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I've been running a campaign for about a month now that is 4d6b3 in order, and we're having a really good time. It can create some really interesting character concepts because of this generation method that you wouldn't see otherwise (17 Int). For our fighter (whose player wanted to play a melee fighter regardless of his 12 str), it changed the way he goes about the game. Instead of standing still making full attacks, he spends a good half of combats looking for ways to interact with the environment to help out: dropping chandeliers, shoving creatures into toilets, forming chokepoints. This method can also make some prestige classes (like mystic theruge or eldritch knight, or heck, monks more viable.
As folks have said above, it works if the players are into it. If everyone is for it but one or two players are against, you could always offer them a different generation method. After all my players rolled their stats, I offered to let them place them in the order they want: no one has taken the offer yet.
It also helps with this method if you lean towards being lenient with what the characters can do. For example, if our 12 strength fighter wants to climb a chain, I let him do it without rolling climb--this prevents some of the problem of someone with lower scores failing at the most basic tasks. During more difficult activities, like climbing a chain in a windstorm while having boulders dropped on you, I still ask for a check.