Mounted physically offensive units seem "okay" to me, so I think there should be a weapon out there to make them better or at least stand out more. Intelligent Systems, if you're listening, I hope you're able to add Cavalry Sabres as a special type of sword in a future installment of Fire Emblem. My idea for them is basically, when used by a non-mounted unit with the ability to wield swords, they're slightly weaker swords comparable to other swords for their level, but when used by a horse-mounted unit with the ability to wield swords, they give bonuses, such as higher physical offense, skill, speed, crit chance, etc. I'm betting this is much more likely to happen then my firearms idea. They'd be a pretty interesting mechanic I think.
Plus, Cavalry Sabres are really beautiful swords :)