ELTs statistically fail to activate in ~20% of accidents. HTAWS were mandated since 2014. It would be interesting to know what type of system was installed and if alerting was disabled.
The elephant in the room is WHY the pilot thought it necessary to check the maintenance log at such a critical point of the flight?
Possibly, due to the accumulated flight time for the day, the pilot feared he could/did overfly an inspection and may have been "check-boxing" it (see my explanation
here). The FAA is willfully ignorant of how it causes accidents.
Just my opinion.