But the lore of the game doesn't consider them pets. Even the official site says:
Nowhere on any official FFXIV site have I seen them refer to a chocobo as a pet, but a companion and comrade. A comrade is a fellow soldier, a partner. Coming from 1.0 and the lore as I understand it, here is an intelligent being that waited years, searching for their comrades return. When we did return in 2.0, they were there to stand by our side and fight with us once again. I don't think I could ever consider that simply a pet. Fellow warrior, an ally, a friend. Yes. But never a pet.When a fellow adventurer's helping hand is nowhere to be found, there are still dependable comrades you may turn to. Fight side by side with your trusty chocobo
Now in the game there is a pet, and a pet bar to control them. Those are the summons that Arcanist, Summoner and Scholar can use.
As for the main point of this thread...
I was just happy when they finally made it to where you could mount your chocobo while you had it summoned. I also appreciate that they tossed in something extra with it. When training your chocobo you get 30 minutes per food. If you mount your chocobo during that time, it stop the counter, so you get 30 minutes of active training time that isn't shortened by travel time as well.
But the only time this issue of not being able to ride another mount comes into play is when someone is training their chocobo, the rest of the time players can use any mount they want. So one might call it the cost of having a fighting companion by one's side that fights, and heals the players character. Plus with people having two mounts out at the same time, that would add massive data to the servers because it would be rendering a lot more. SE already is crying 'technical limitations' one year in due to servers, I don't know if they are going to want to add a heavier load to that.
But if SE feels they could do it, then that would be up to them to decide.
Now if this is about wanting to use a favorite mount, wouldn't it be better to ask them to allow leveling of the mount of players choosing? Players can pick ONE mount to level, just like a chocobo. And this ONE mount would be your fighting companion. But then again, and I think people know this, favorites change at a whim. If/When SE presents a new mount, then comes the 'but why can't we change mounts and move the stats, because this one is my favorite now'.
I believe that is why they chose one mount that players can level and chose the Chocobo to be this companion. It is highly recognized and an icon of FF lore. Personally my chocobo is my favorite, and I adore him. Even if I'm not training him, he is the one I ride because he's my comrade. But that is just me.
As for the glamouring of a mount, I'd have to agree with others. Glamouring our clothes is one thing, but making a whole animal look like something else is a totally different thing. I don't know if I can agree with that one.