maybe the question is not why there are different techniques for required tasks.

rather, why do CFIs, who are giving checkouts and BFRs to experienced pilots (as opposed to primary instruction), demand one specific method?

Shouldn't they use the "Satisfactory Performance" criteria as outlined in the PTS, which says:

Satisfactory performance to meet the requirements for certification is
based on the applicant's ability to safely:

1. perform the TASKs specified in the AREAS OF OPERATION for
the certificate or rating sought within the approved standards;

2. demonstrate mastery of the aircraft with the successful outcome of
each TASK performed never seriously in doubt;

3. demonstrate satisfactory proficiency and competency within the
approved standards; and

4. demonstrate sound judgment and ADM.

--bob