This is awesome... Why couldn't we have this?

[Felis]

Ascians are not the reason why they summoned the Primals, they merely taught the bestmen how to do it.

The Ascians don't just teach, but also create the situations where the beastmen use what was teached to them.

As an example:
They worked together with the Allagans. The Allagans went on a dragon hunt, killed Bahamut and captured Tiamat.
And the Ascians teached the Allagans how to capture primals and teached Tiamat how to bring back her dead lover as a primal. The rest is history.

[Atoli]

The Ascians don't just teach, but also create the situations where the beastmen use what was teached to them.

Yeah, they stir a bit of chaos. But honestly, at this point, with the aftermath of Dalamud and the like, their is enough chaos to have lots of conflicts even without them meddling all that much.
And it's not like we have someone on the opposing side who actively tries to calm said chaos...

Edit answer to your edit:
See how the Ascians never did anything bad even in your example though? They just showed people a path they could take and they readily went down there, even though they always had the option to choose otherwise.
That's partially why Thordan was so interesting to me for quite a while - because he planned on USING the Ascians, to take all they could offer and still not go down the way they wanted him to go. Sadly, he ended up doing it anyway. But yeah, you always have the option to ignore the Ascian's whispers. Except for the final fights of both 2.0 and 3.0, the Ascians never personally try to go against "the light" or her messenger. They just tell people "you can take the dark path too" and that's it.

So I still see the problem in the circumstances that force people to make a decision between Zodiark's and Hydaelyn's way in the first place.
Basically, if everyone was 100% happy, well-fed and so on, the Ascians could try to manipulate as much as they want - no one would bother following their teachings.