nuisance value 
noun [mass noun]
The significance of a person or thing arising from their capacity to cause inconvenience or annoyance: his potential nuisance value as a dissident minority shareholder...
- The nonchalance with which that episode is recounted lends a surrealistic edge that is all the more pronounced because Richards declines to tell us anything of his feelings about his disability, except to complain of its nuisance value.
- It was strange, because before that injured players who could still walk were left out on a wing for nuisance value.
- But that is churlish and does not do justice to the magnificent Australian defence, the great running lines and talent of their backs and aggressive nuisance value of Justin Harrison.