Right, the mount ”rules” look to be designed to add onto to the 5e rules, not replace. And it’s not an adding of complexity IMO, any more than adding any a player-controlled monster is adding complexity.
There are 6 mounted-variant monster stat blocks, for variants of creatures that were raised from birth to be mounts. Basilisk mount, giant toad mount, hippogriff mount, nightmare mount, owlbear mount, and warhorse mount. So not the full blown owlbear or basilisks that are encountered as wild monsters, but trained mounts. These mounts all come with the “mounted” trait in their stat block.
All between CR 3 and 1, they get extra stuff when ridden by their rider like better AC, Saves, and some temp hp, for example. But riders can use their bonus action to command their mount to do a variety of actions from their iconic attacks, to some 1/day or 3/day actions. Even warhorse mount has a 3/day and 1/day actions that fit what you’d expect a cool ass hero horse to do.
The dismounting attack for the rider is an obvious cool idea.