Under this point of view a FI training limited to LAPL is totaly useless!
Not so... the LAPL should eventually become the default qualification for people wanting to learn to fly.... I am surprised that (in the U.K. in my experience anyway) there are few schools offering it.
No, HPA does not qualify as TK for CPL.
The full FI course equips the applicant with the skills to assess the ab-initio exercises - the CRI course not so. The only thing a CRI can do that an FI can’t is in the initial stages where the FI is restricted they must operate under supervision of an ATO/FI. A CRI has no such initial restriction.