It’ a 4th level spell. It’s in the same class as Mordenkeinan’s Faithful Hound and Charm Monster, both of which make a minion that can attack at will. Also, only two classes can get it: the Paladin, and the Bard. The Bard can get it at lvl 10, due to magical secrets, but the Paladin, who this spell is for, can’t get it until level 13 at the earliest. At this point, Wizards are casting Force Cage, Plane Shift and Simulcrum. And you’re getting uppity because he might have a flying mount that he can command that can have its own initiative?
Mount rules would apply, I presume. According to the player’s handbook, you need:
1. A willing creature at least one size larger. The spell makes this
2. When in combat, you have the option of controlling the mount, or letting it act independently, but intelligent creatures act independently. This means they do their own thing.
3. You can control a mount that is trained to accept a rider. The spell makes one of these.
4. The initiative of controlled mounts change to match yours when you mount it. It moves where you tell it to, and can Dash, Dodge or Disengage.
5. An independent mount (including all intelligent mounts) retains its own place in initiative order, and can take whatever action it wants. It moves as it wishes.
Now let’s look at the spell:
1. Summon a loyal majestic mount
2. It gains an intelligence of 6 if it does not automatically have one
3. You control the mount in combat
The rest is incidental. What I take this to mean is that the mounts are intelligent, so they act on their own initiative place and can do whatever actions they want, but as an exception to the normal rules of mounting, the summoner controls it during combat. Remember, specific trumps general. Note, the third point is NOT included in the normal Find Steed spell. This, to me, indicates a change. Some of the main differences to these mounts from normal steeds is they have special abilities. What is the point of having special mounts who can use flyby, charge people with a horn, or rake them with claws if you’re not allowed to actually use these abilities?
It’s a pretty high level ability, which most players won’t even get to. Bards get to it a little quicker with Magical Secrets, but that’s it. I see no problem in letting them use it the way they want to. You can always do what my DM did when I abused my Winged boots: he had us be attacked by a flock of griffins. And I was alone, cause I was flying all over the place. Scared the bajeezus out of me. If you don’t like how they use it, don’t nerf them, give them a challenge meant to counter what they are doing.
And about having them attack independantly, I don't see why they couldn't. In fact, now that I'm looking at it, i'm a little confused by your post. Are you saying you don't believe the mount should be able to attack without being mounted, but when mounted they shouldn't be able to attack? Forgive me, but that seems to reduce the spell to a cosmetic upgrade from Find Steed, where your mount is basically a larger speed number.
The mount is a creature that does what the summoner says. It should be able to attack regardless of whether or not it is mounted, in my opinion, but certainly when it is not mounted. There is literally nothing that says it shouldn't be able to attack when not mounted.