You're very right that the status quo won't last, but that tends to be a pretty major theme of the story I'm trying to tell, I think. Anyhow, the Khirichan have survived a number of incompetent Khagans who slid largely under the radar between Sebouk Arslan and Shiqar Kulujogul.
I hope it doesn't seem like the Frankish empire exists just for the sake of "space filling." I've tried to make it seem like a diverse country with lots of regional interests.
The Khirichan political system possibly deserves its own post, but in short, any measure of the stability of their state has to take into account more than just the personal qualities of the ruler who runs the show. Even in the most basic tribal polity that's true, but the Khirichan have transcended that pretty seriously by now, taking their cues from the Sahu and Eftal, who in turn were inspired by a variety of Indo-Iranian sources. They're a settled state for most intents and purposes, with cities and a capital and taxes. Their relationships with the other clans and subject polities that make up their regime have evolved to the point of being codified lists of reciprocal obligations rather than just extortion and tradition.
(Which is not to say that their relations, particularly with Europe, don't involve a lot of extortion and plundering. Just that the core of the Khirichan state is strong.)
The Khirichan are undoubtedly overstretched. But I will say this: it's a lot easier to keep the Xasar and Bulgars and Russians all in line when the alternative is an existential threat on the scale of Frankish Europe. On the same note, it's a lot easier to keep Spain, Italy, France, and Germany all in a line when you can remind people of the scary scary specter of Sebouk Arslan or Kuluj Ishbara and all the other threats from the diabolical East.