Many contractors/companies have databases or files full of risk assessments for their tasks and activities. These would be classed as generic risk assessments. They may be specific to the task or activity you are carrying out, but they are not specific to a particular site.
There is nothing wrong with having files of generic risk assessments, in fact, it is good management practice. Better to have a risk assessment template to work from, than start from scratch each time. After all, most of the hazards and consequential risks associated with say, plumbing, will be the same wherever you are working.
But that’s most of the hazards and risks, not all of them. Site specific risk assessments take into account the actual site conditions and type of project, and address only the relevant hazards.