There are a number of LABCs that will accept a PIR, and there are some that will only accept 3 part EICs.Doing so does not mean that they are not partaking in the enforcement duties of Part P, in fact it indicates the oposite.
Remember there are two methods of compliance with Part P, one is to pre notify and pay the relavant fee, the other is to employ someone who is registered with a self certification scheme.
Insisting that someone who has failed to notify or employ someone regisistered, should notify retrospectivly and prove compliance by producing an EIC or PIR (which ever is acceptable) is to my mind enforcing Part P.