@Kinematics , what are your thoughts on the more "advanced" mounts - f'ex, my Paladin is currently riding an Allosaurus, which has a rather vicious bite attack. How would you handle it's attack ability? I'm thinking a bonus action to use the mount's attack routine, but thought I'd bounce it out here. Likewise, other monsters including griffins, manticores, wyverns, dragons and the like.
I had to take some time to think this over.
My first thought was to adopt a little of Level Up's mounted combat, which has refined things from O5E. An O5E mount can only Dash, Disengage, or Dodge, though it doesn't require any action on your part to allow that. A5E allows you to direct your mount to make an ability check or take the Attack action (but not multiattack) by using your bonus action.
Allowing this can make a mounted combatant quite a bit more dangerous. A warhorse would get a 2d6+4 hooves attack, and an allosaurus would get a 2d10+4 bite attack. Getting that as a bonus action feels a bit overpowered. On the other hand, it certainly motivates the enemy to knock you off your mount.
There's also special actions, like the allosaurus's Pounce, which has a chance to knock an opponent prone if the allosaurus uses a claw attack and the enemy fails the save. (Same for the warhorse's Charge.) Those abilities also give a chance for the mount creature to make a bonus action attack if the knockdown is successful, but that aspect certainly shouldn't be available during a mount action that is itself a bonus action. But the knockdown itself does feel like it should be possible. (Putting aside whether you would then be able to reach a prone opponent with your own weapon.)
Level Up makes that distinction moot in most cases, because the extra effects are tied to the basic attack in the first place. For example, the warhorse just has its Hooves attack which can knock prone if there was sufficient movement beforehand, and not a separate Trampling Charge. Since that seems mainly like a clarification of the stat block, let's just assume that to be how things generally work, though also ignoring any potential bonus action attacks.
Then we have to compare it to another very similar class situation: the beastmaster ranger. With Tasha's update, you can use a bonus action to get the companion to attack, and you can sacrifice an attack when you take the attack action to also get the companion to attack. However the companion's attack damage is 1d8+2+PB (so between 1d8+4 and 1d8+8), which, even at the high end, is less than the allosaurus's bite, and only a little ahead of a warhorse's hooves.
This feels (again) overpowered... except that the ranger is entirely capable of making use of this as well, and still be able to also command its companion. So...
How about this: If you have proficiency in Animal Handling, you may sacrifice one of your attacks from the Attack action to command your mount to make an attack.
You'd be sacrificing an attack to get the mount to attack, but that can be a good trade for damage, and often a bonus effect. It may not be as useful for lower-end mounts, though. For example, a pony in A5E does only 1d4 damage (it doesn't even add its strength, for some reason). A mastiff is probably better for small characters, since it does 1d4+1 and has a chance to knock the target prone. In O5E, a pony does 2d4+2, while a mastiff does 1d6+1, with a chance to knock prone.
I'd be fine with using a bonus action for commanding the attack if all mounts stayed at the low end, but the high end and exotic mounts feel way too imbalanced if that is allowed. Maybe: Starting at level 5, if your mount is CR 1/4 or less, you may use a bonus action to command it rather than sacrificing an attack.