Well dang, they actually listened. (Primal birds)

[Zojha]

So in total I did 393 runs of all of them to get all 5 birds.

Aaand with the 99 tokens, you'd do 495 runs to get all 5 birds. Sounds...more than fair, really.

And yes, it is all luck - you "can" go a billion times and never even see it drop, let alone win the roll. You "can" have it drop on your first clear and win. RNG is never an achievement.
I agree that perseverance is - but for that it doesn't matter if you were successful or not in the end. Your achievement are not the 5 birds, but the 393 runs. Anyone with any combination of birds and the same amount of runs achieved the same. Some are just more or less lucky than others, hence not the same amount of birds.