Can compulsions be defined in a way that is independent of obsessions, culture, etc?
The fifth edition of the Diagnostic and Statistical Manual of Mental Disorders (DSM-5) includes a new chapter on Obsessive-Compulsive and Related Disorders to reflect the increasing evidence of these disorders’ relatedness to one another and distinction from other anxiety disorders, as well as to help clinicians better identify and treat individuals suffering from these disorders.

You are right that compulsions are


  repetitive behavior/thoughts intended to reduce distress and/or
  prevent a potentially serious situation


and this definition can be used for compulsive behaviour which does not pose a problem.

In this chapter the DSM is talking about disorders which in turn means we are talking about unjustified or socially unacceptable behaviour.