Considering the number of times I've won Leviathan EX (well into triple digits) and how often I've seen a mount (or a mirror), I think it's fair to say that the drop rate is 1% at worst and no more than 5% at best (probably wishful thinking there).
Are people actually expected to want to try to obtain these items?
Assuming an "ideal route" of forming a static with the express purpose of farming these mounts (because if you're relying on randoms it's going to take way, way longer unless you're super lucky, what with the losses added in and the possibility of infinitely losing lot to a revolving door of contenders), you and your 7 suddenly closest friends will need to complete about 800 wins per EX primal to "guarantee" drops for all 8 of you. Naturally 8 mounts could drop in less wins than this, but assuming a statistical average, it's not unlikely for it to be 800 (or, you know, way more).
So, that's 800 x 5 for 4,000 wins across 5 primals. We'll assume that Nightmare will drop for everyone in the middle of farming the mounts specific to each primal. Let's further say we're averaging 10 minutes per win. You can definitely shave time off this number for some/most, but honestly you'll probably still take breaks, have an occasional loss, and otherwise fail to queue back to back wins for the entire duration with no downtime.
That's 40,000 minutes. Or 666.66~ hours. If you do this for 40 hours a week (hey, you just found a new job!), it would take you approximately 4 months for you and your group to obtain every primal mount.
Does this strike anyone else as sort of, you know, ridiculous?
(Oddly enough, the time it would take to farm up 1 primal mount for your entire group is the same amount of time it would take to win trade to PvP rank 40.)
If everything in the game is super grindy, from actual content to vanity stuff, eventually people are going to get sick of it and unsub. Certainly I'm questioning why I haven't, because we seem to be steadily heading FURTHER into the realm of intense grinds and 1% drops. If you actually wanted to do everything in the game, you'd probably quickly become 1-5 years behind current content because you were too busy farming old content due to ridiculous drop rates, etc.
I'm sure right now someone is frantically typing out something like "Then it would be too easy!" or "It's just vanity." or "Then it wouldn't be rare!" or "If you don't want to do it, then don't!"
Well, if SE doesn't want people to do X content, maybe don't put it in the game. And if they want something to be rare, gate it behind skill, not luck. An example of this done correctly is the new titles for completing Second Coil (Savage). Rafflesia Reaper and Melusine Mauler are just about the first actual cool titles in the game, and to get it, you just, you know, beat those turns of Savage. If they were analogous to primal mounts, it would be beat Savage Coil Turn 2 for a 1% chance at a title. Oh boy! Time to beat it 99 more times, because that will prove I know the fight, right!?
Long story short, if SE doesn't want you to forget about friends, family, school, or work, why do they seem bent on ensuring someone dies in an internet cafe trying to get a bunch of stupid 1% drops?