@ErinOwOErin As one of the earliest MMORPGs - indeed it is credited with coining the term - Ultima Online was a very unbalanced game, at least as it continued to add more and more content and change more and more existing gameplay concepts to attempt to stay relevant in the evolving genre.
In real life (who cares about that am I right), not every fighter who rode was actually trained to fight on horseback, nor was this necessarily intuitive or better when they were - the zweihander and other specialized weapons were designed specifically to confront riders.
In many MMOs, you're not even allowed to fight mounted - your mount vanishes when you enter combat and must be summoned again afterward. (In Elder Scrolls Online, your mount's stamina acts as its HP, and you're dismounted and Stunned if it expires from an attack. IIRC you can get a perk that makes your mount not use any stamina ever to last longer in combat.)
But in the MMOs where you can fight mounted, it is almost always a complete improvement with no downsides to do so. You move faster, you sometimes hit harder, and you almost always get an HP boost. This means that absolutely nobody "competitive" will ever not be on a mount, and therefore, everyone will have these giant gaudy show-off mounts the way some games let you get massive stupid-looking angel wings and auras and rainbow-colored armor.
The only time I played Ultima Online for more than a few minutes, I was ambushed by over a dozen high-end PKers all riding huge, six-legged "swamp dragons", who cornered me the the same as if it was a dozen dudes on foot piling up on me to punch my ribs.
Mounted combat can easily make an MMO look completely ridiculous and generally introduces a huge power gap, both of which can turn away basically all players other than min-maxers.