Wha? I’m confused by this. What about, like, 会社 (かいしゃ) or 神社 (じんじゃ)? I suppose they’re third mora here… but still final, not initial.
EDIT:
医者 (いしゃ), what about that?
EDIT 2:
OK it’s occurring to me the quoted analysis was perhaps about mora within individual kanji readings, and not about mora within words.