A speaker cabinet's grille cloth and speaker cone are both surprisingly delicate compared to the solid-feeling wood box around them, and setting anything heavy on the cone side is one of the fastest ways to damage a driver. Protecting the grille and controlling what rests on top covers the real risk.
Pro tip: If the cabinet has removable casters, take them off for the move; a caster that catches during a tilt is a common way cabinets get dropped or dinged.
Watch out: Never set boxes or other gear directly on the speaker-facing side of a cabinet; even moderate pressure on a cone through the grille cloth can dent or tear it.