Me? I vary in my opinion on rares and uniqueness as there is many variables. Lets see pros and cons.
One of a kind creature that has a different appearence then others, so people usually know its it by name and they oooo and ahhhh and squee and v.-.-.v
You work hard to find this creature, the thrill of the hunt, the beautiful sounds of the scare-the-crap-out-of-you npcscanner
The beating heart as you try to recall where your tame beast is and your trap, only to realize your full with pets and so begins the larger heart beat cause he'll be hard to find again since you dont have the option of taming the skin on a common
The bond you created from all the heart ache of having no choice but to camp said pet for so long
sitting, staring at the screen for all hours at ends/days/weeks/months
the competition who have this idea it may be better to kill it then to let anyone else have it
finding its corpse, brought to you by the people who think silver portrait = epic
you may not click with the skin but dont want to release it because of how difficult it was to find
Non unique rare
You dont have to camp hardcore for the skin but you have the option to do so
You can tame a non rare to see if you like the skin in the first place then go out and tame the rare if you so choose so
You can switch out to a regular skin when at the area of the rare so people dont cry when npcscanner goes off but you still have your favourite skin out
For some can be less thrill of the hunt
For some it feels less epic when you do find it cause you just ran into the skin like 10 mins ago while running around in Mop and his relations tried to kill you (you will at this time missing flying until your lvl 90)
For some you miss the whole SQEEEEEE where did you get that it is so awesome and the whole joy and joyness of telling your story
Thought of some ideas
Can make the non unqiue rare a challenge tame so its more thrilling to hunters.
Can make the unique rare a slight variation of coloring instead of a whole new model, like instead of Sambas who is the only lion like that, you can make the white tiger a rare but have the grey variation as a common.
Can also add different highlights, like make brighter eyes, a glow etc on the same skin that a common has.
Also can make the timer not as hardcore as 12 hours and instead switch it between 2-6 hours, that way casuals have more of a chance to get the rare.
I like some of those ideas, and I think they would go a ways towards possibly reducing the number of rares. But I think there do always need to be some.
Playing off your idea...
Have 3 models of a pet.. one common (easy tame), one rare (looks a bit different), rare challenge mode tame (even more special look). Yeah, I know it will never happen, but...