As it is, there are many members, yet one body. (1 Corinthians 12:20 NRS)
Now you are the body of Christ and individually members of it. (1 Corinthians 12:27 NRS)
Other than in B-grade horror movies and perhaps the occasional bad dream, body parts acting on their own, separate from an entire body, are not typically the norm of everyday life. There is a vital, life-giving connection necessary for each part to be sustained by the body. When that connection is weakened or compromised, or worse yet, completely severed, the ability of that part of the body to function is threatened or lost. A body is an interconnected, interrelated, interdependent system, not a random collection of pieces stuck together without a unified purpose. Although the various parts may have different functions and abilities, they simply cannot exist without a primary body (sci-fi/lab experiments notwithstanding).