A few too many assumptions here
The reason I have at least 2 tamers per shard I'm involved with (Chesapeake, Europa and Atlantic) is because I kept running out of stable slots. None of them are Gargoyles because, well, Gargoyles can't ride. Sorry, but you gotta ride

The majority of pets are mounts after all.
So what the heck am I doing with all those stable slots? Dare I reveal that little secret about true tamers in Ultima Online, knowing you'll think we're all nuts? What the hell...
Tamers in UO - the bonafide ones - may know, intellectually and rationally, that in-game pets are a mixture, a concatenation of code strings directing pixels and such to digital action. Nonetheless they regard their pets as ALIVE. Our pets are living things. They are.
And I'm fond of mine, from my crew of five frenzied Ostards and their cacophonous compliance to every command, to the many massive, meat eating, magic casting black steeds known as Dread Warhorses that I've collected over the years, to the menacing hiss of Rune Beetles, the portentous laugh of Bake Kitsumes. There are those Cu Sidhes that heal themselves - and me at times - with bandages, the satisfying base rumble of a White Wyrm's voice to....you get the idea.
When I was doing an Orc prison compassion run one day I saw an abandoned Kirin just left there, gamely fighting off Orcs. What was I supposed to do? Just leave it? I am the product of a live birth and a living soul, my friend. I tamed that charming, forlorn creature and departed the cave with the now renamed Lost and Found. I stabled it. And, when it bonded, I trained it, GMing even its magery. Marvelous magical long maned animals, the Kirin.
But they are not my favorite. That would be the Hiryu - pronounced Hear-You. They come in many colors, all of which I possess an example of. Further, in farming and taming them, I selected not only Hiryus with bright hides; they have high stats and every one of them is curse tamed as are many of my Cu Sidhes. The Hiryu is the easiest pet to work with because its range of visibility is longer than any pet in the game. Tell it to guard you and it will move to threats screens away in a blink. It can see farther than you can. They are stronger than most Greaters (700) and if they have high intelligence they'll almost spam their specials: dismount and armor corruption.
Yes the Greater Dragon is a useful pet - against a monster. Some pets are particularly good, and far better, at killing people. A Rune Beetle can have eval as high as 112 and poisoning beyond legendary. And, given the extremely mobile nature of that sort of fighting, their very high dexterity (up to 170) means they can keep up with their owner, riding a Nightmare, at full gallop.
As for poisoning, though, nothing is quite like a Bane Dragon - technical designation: Dread Swamp Dragon. It's hard to get any high stat animal but, in my experience, the Banes were the worst....hours, days, weeks in the Abyss, in that temple complex of Slasher's, farming and farming to find fine examples. Their statistical package matches that of the Dread Warhorse whose mana can go as high as 165. But the Bane is a difficult beast. Crude too. Fed with blackrock stew it just spews poison - often deadly poison - EVERYWHERE. I've seen them poison people or things standing BEHIND it.
More subtle is the Skree. It uses Mysticism and Sleep. Strange little green creatures, the Skree.
Yes, there are some pretty useless pets. The Fire Steed's difficulty in taming - largely due to its location - feels uniquely unrewarding. It's not very strong and its pack instinct is not effective. Same for Raptors.
In truth, I don't use most of my pets anymore. White Wyrms are probably the best example of pets kept by tamers for sentimental reasons alone. But I have a fondness for all of them. Thus, I have plenty of use for all those stable slots
A full stable is the prize of much patience, and many, many years.