Upon analyis, nothing can be done using cryptographic techniques for to prevent the fraud by theft of identity - if a fraudor learns and remembers every relevant identification data about his victim, he can impersonate his victim, e.g. in applying for a credit card.
The main countermeasure against the theft of identity is care and discipline in the verification of identity upon application for a new service. With the SAKEM procedure, any such effort put in the verification of identity is directly reflected in the level of confidence in the secret key (the very outcome of the procedure).
Moreover, the SAKEM procedure can be arranged so that the issuer agent who verifies the applicant's identity is in a good position to relate to the applicant (e.g. a bank branch employee), in which case the theft of identity is harder to achieve.
So, SAKEM supports the "best practice" against fraud by theft of identity.