alas
唉 centers on a vocal expression of sorrow or regret: an exclamation like 'alas' or a sigh of lament.
唉 combines 口 (mouth) with 矣, which likely contributes the sound and may relate to an exclamation. The exact historical development is uncertain.
The mouth 口 beside 矣 suggests a vocal sound. Picture a mouth open in a sigh, letting out an 'alas'.
For カイ, imagine a sad sigh that sounds like 'kai' — a mournful cry: kai -> カイ, matching the 'alas' meaning.