Many times, animals are suffering from a disease, although that may not be why they're becoming a nuisance.  IF there is $$$ available to test for all communicable diseases the animal may have, then relocation is warranted.  HOWEVER, that can be very expensive, and so many wild animals who have become nuisances are just euthanized.  It makes no sense to relocate a sick animal and infect other animals in a new location.