I now believe the reason why A9 does not support HEVC and HEIF. Performance is not enough.
I have a few video clips encoded as HEVC. While watching it, the phone becomes hot and battery drops low rapidly. I am using iPhone 6s Plus. A9 is just not powerful enough to decode HEVC content efficiently, let alone encode.
Apple has complete hardware level support for HEVC and HEIF in A9 and up.