There are some situations where it is better to build battlefury, but it is massively overbuilt on alchemist in games where radiance is much better.
Radiance deals damage regardless of whether or not you are stunned, controlled, or kited. You must hit something for battlefury to deal damage. Unlike antimage, riki, or PA alchemist has no built in way to get 'on top' of a target, meaning it's more difficult to put him in a position where is constantly hitting his target and benefiting from battlefury.
Alchemist does not benefit from the increased regen provided by battlefury. Building a soul ring is enough to ensure he can consistently cast his spells and chemical rage takes care of hp regen.
Alchemist already has a cleave talent.
Alchemist can fight early on to a certain degree if he builds radiance, he cannot do so if he builds battlefury.