You may not have to have done the CPL flying course but as a practical matter you will need equivalent to CPL flying skills before you start the FI course.
Although there may well be a significant number of
experienced PPL holders with practical knowledge, relevant experience and light aircraft handling skills in excess of those possessed by inexperienced CPL holders.
At the end of the day, those good enough will pass the FI Skill Test regardless of their background. Although I agree that, in general,
inexperienced PPL holders are unlikely to be able cut the mustard.