According to your original point, about mounts being "pure pve territory", you're shooting yourself in the foot by posting the census. Of the 70 existing mounts, 6 are from PvP. Given how miniscule a part PvP plays in this game, it has a disproportionately large amount of mounts obtainable through PvP content. Fancy that, maybe SE is encouraging PvP content through provision of rewards.
The fact that PvP mounts are rare has more to do with its popularity with the kind of playerbase we have. SE has tried, through providing different PvP content with varying objectives, to cater to different groups of people. The latest, as you know, features a more relateable PvE-experience (the reception to this new mode is a different discussion entirely). PvP activity continues, largely due to its small, but dedicated, community of regulars.
Regardless of this fact, if the existing--fully available--PvP mounts are rare (exclusive, by your wording), making the upcoming exclusive (as indicated by SE on the Feast promotion page) Top 100/30 mount "fully available" won't greatly (relatively) increase its occurrence. It will only serve to insult the, again, small but dedicated PvP community, and dumb down the hype surrounding the individual seasons we have right now. That's bad for the content. Providing the carrot that drives us is our incentive to win the competition. I say this as someone who is not in the top 100 this season, and probably won't make it. I'm totally cool with that.
I wear my S1 top 100 PvP gear on the only jobs I play, SMN and the occasional AST. I have different sets for DoL and DoH, respectively.
I have the Gloria-Class Airship as my mount for every job except DoL jobs, that use a plant for BTN (Cloud Mallow), a water birb for FSH (White Lanner), and a fiROCK birb for MIN (Rose Lanner).
I see other people occasionally on PvP mounts on the way to hunt monsters, so they're out there.
This kind of thought, to me, is disgusting. In any competition, there will be winners, and there will be losers. It's rewarding and motivating to have wins and losses both, especially if the competition is skill- or talent-based. The grand prizes are for the winners, there already exists consolation prizes in the form of accessories and titles, not to mention random minion drops, PvP-specific currency for non-competitive rewards (weapons/gear/music/minion), and PvE currency. There's even 2 seasons for similar (but not the same) rewards for a second chance. That's more than enough handouts, stop asking for more.
Besides, there's nothing wrong with "missable" content. You already have that with many event items/titles, all 1.0 stuff, collector's items that require something like initial release only, etc. You don't have a leg to stand on.(Ty Tira)