A reasonable rationale for why let-else doesn't have let-else-if is a combination of:
Because the let introduces a binding into the containing scope, the else clause is required to diverge. Due to this, it's not at the same "level" of control flow like the various conditions of an if-else-if are.
Avoiding ambiguity for the human relies on } else always being the else of an if-else, and never a let-else. This would break that property.
My baseline response is that the this could make sense, but is ultimately driven by just a desire to remove syntactic nesting instead of allowing the code to better correspond to the logical control flow structure.
let-else-match isn't exclusively about reducing nesting; the claimed value-add is that the match retains access to the scrutinee on failed a pattern match whereas let-else drops it.