Mounted combat has a lot of problems in D&D. Nearly all of them have to do with the simple fact that horses don't belong in dungeons. They're so limited compared to a humanoid. Mounts don't like narrow passageways. They can't climb ladders. They can't use spiral staircases. God help you if you need to travel the planes. If they fall into a pit trap, they're 1,000 lbs of dead weight stuck at the bottom of a pit. Their high movement rate is often totally irrelevant indoors, too, and you'll be bottlenecked by doorways and rooms. A mounted knight doesn't exactly fit through a doorway. Even outdoors, their tactics don't really provide any benefit at all if the creature can fly or has any kind of special movement. They don't like uneven or steep terrain, either. Paladins have it slightly better with Summon Steed... but it's still difficult to make work and Summon Steed isn't quite the Pokeball it really needs to be like Find Familiar. So you can focus on mounted combat, but there's a significant risk that you're just going to have all this investment into stuff you can't use.
It's a lot better for small characters if they're riding a more agile animal like a dog... but One D&D just made lances heavy. So... guess that's that?
I played a Paladin from 1998 to about 2004. Started in 2e AD&D, converted to 3e D&D, and then to 3.5. Went from level 1 to level 15. I never once called my steed. I just never wanted the obligation of a mount to take care of, and there was no benefit to having a mount. We spend 90% of the game in the underdark, lost across the outer planes, lost in untamed wildernesses, or in various urban settings. Our DM was a big fan of Chronicles of Amber. I remember the first dungeon we went to at level 1, the NPC that hired us gave us pack animals for the journey. The party ended up drawn through a portal in that first dungeon. We never saw those pack animals again because we never returned through the cave entrance.
Mounts are too much of a liability.