Yeah, after playing today I had the chance after getting knocked out early to watch cavalry try to do their thing, emphasis on "try."
I feel like it's partly thanks to the AI actually being too good at defending against cavalry. As soon as they so much as see a horse they'll pack in tight with a Shieldwall or Circle formation that protects the archers and entraps anyone foolish enough to think they can charge through without getting stuck by the mass of bodies or a spear causing their horse to rear up. It's usually a different story if the enemy is engaged in combat, but like you and LDominating said, Vlandian infantry will start loosing badly if the matchup is poor, taking massive casualties long before the lancers can make a meaningful dent in the enemy numbers.