The answer to that question is more easy:
You have to see the sword as a side-arm... a secondary weapon... like the modern pistol on a soldiers belt.
A real sharp sword is as light as a pistol and it has the same use: to defend yourself when your primary weapon is gone/useless.
The primary weapons for fighting on horseback are armorbreaking weapons like lance, hammer, morgenstern, streitkolben etc.
A sword >can< have an effect against armed enemies... but it is more effective against unarmed enemies.
A knight always wears his sword on his belt. It is not as heavy as the decorative pieces you may know from modern medieval events.
My sharp longsword is as light to handle as a kitchen knife.
I can recommend to read Bernard Cornwell`s "Azincourt" to get a feeling for using medieval weapons.
I have studied history and it is a often used reference.
The reason why I primary do sword photos is: The other weapons are very expensive, I have no horse, the sword is also connected to the romantic myth of defending the weak... which is the primary motive for fantasy pictures and book covers.