Firstly, they just look tacky. Secondly, they imply a statutory power conferred to the holder which, unlike for the police and other agencies, doesn't exist. Lastly, depending on how you use it, you might end up charged with impersonating a police officer (say you flashed the badge at a witness who didn't look too closely, didn't state you were a PI and then they naturally assumed you were a police officer...)
If you need something, I suggest a copy of your licence or accreditation should be enough.