Why is the dichotomy "Carolingian Empire united and relatively centralized and powerful" on the one hand and "collapse into civil war and eventual territorial division" on the other? It's exceedingly improbable that the Carolingian state could keep expanding and conquering and so forth indefinitely, and the Wends, proto-Poles, Moravians, etc. weren't exactly pushovers. Dynastically, there's basically zero chance that the Franks can keep a perfect streak up, and they've got virtually no civilian or military bureaucracy to fall back on in the event of a stupid heir (or no heir!). I can't see the state expanding
or integrating successfully (remember, the East-West Francia division didn't fall out of the sky; as soon as you get further west and south than the Rhine Valley you simply don't see many Germanic dudes) for much longer than a century at the outside, if the Frankish succession laws are theoretically dumped
and nobody manages to win a civil war anyway. (Because large, insufficiently integrated empires can collapse into little tiny pieces even without stupid ways of dividing the property of dead men. True story.) Anyway, the best way for this monstrosity to survive is to a) stop expanding and b) start decentralizing, whether by accident or design. Maybe after a few centuries of that, the foundations will be solid enough for the state to actually
do something. (And, when it does, it'll probably collapse anyway.

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After the death of Basil II (apparently called Bulghar Slayer) he left no heirs due to his paranoia and there was some bickering and infighting, and his successor was underwhelming and an alcoholic who didn't do much of anything so they gave him the boot after a bit. The Byzantines became preoccupied with internal affairs and mostly ignored the East. When Sultan Alparslan and Emperor Romanas IV were on the throne something inconvenient called Manzikert happened, it was all downhill from there.
(Insert this space for where Dachs tells me I'm wrong about something and then writes an essay to elaborate)
Pretty drastic oversimplification, but more or less right. Mostly. (I wasn't aware Romanos III Argyros was an alcoholic. That wasn't his chief problem, anyway, much less the empire's. The chief problem was the succession problem you mentioned and that damnable Zoe.) Though it should be said that, among the many things they did, the Byzantines emphatically did
not ignore the East. Territory was actually conquered in the Caucasus for a few decades after Basil's death. The big problem that the empire had, actually, was that its leaders did too much in the East, and in too short-sighted a fashion. Basil had left a ring of loyal tributary powers from Syria to the Caucasus, both Christian and Muslim. His successors, seeking cheap victories (part of a legitimacy problem; they had to appear as though they were commanding the army as Basil had, but none of the emperors were competent generals, since if Zoe had married a competent general he probably wouldn't have let her blow half the treasury on clothing, perfume, the 11th-century version of Botox - I am not making this up, she supposedly had no facial wrinkles even when she died - and "eunuchs"...anyway, they had to pick targets that were easy to beat, and the only ones of these were the tributaries that previously had been an invaluable force multiplier for the Byzantine army), attacked these tributaries and paved the way for the Seljuqs and Turkmen to swarm in and start raiding, beginning in the 1040s. Defenses were further weakened by extraordinarily short-sighted economies and cost-cutting measures, enacted in large part because the Crappy Emperors Who Married Zoe weren't competent enough to defend themselves from rebellion, so if you're going to have to downsize a part of the military, might as well make it the part that's most dangerous, right? The guys who are well-trained and battle-hardened from fighting on the Armenian frontier? Which is where the Turkmen would decide to start raiding in the next few decades? Aaaarghhhhhh...
It's also worth noting that Manzikert itself was comparatively unimportant. No matter what happened there, Romanos IV would have been stabbed in the back anyway, and in all other respects the engagement was more of a skirmish than anything else. The army itself suffered virtually no losses, and Alp Arslan was a dude who was rightly uninterested in worthless mountain territory when he could play for Egypt instead, so he demanded little and let Romanos go. What screwed the pooch was the series of civil wars in the 1070s - which, it must be said, probably would have occurred no matter what had happened at Manzikert - that simultaneously ruined the Byzantine army and brought Turkmen into Anatolia, ostensibly fighting for one side against the other and conveniently electing not to leave when their job was done. (The same thing brought the Ottomans into Europe, actually - a position that they sure as hell wouldn't have been in, had not the Kantakouzenos-Palaiologos civil wars not kicked off. I am convinced that Alexios Apokaukos, who started those wars, was reincarnated in the form of Al Davis, with the Turks played by the New England Patriots.) And, of course, we should give honorable mention to Alexios I Komnenos, who is best known for saving the empire from certain doom and for handling the Crusaders without much damage (and rightly so), but who, when he had Anatolia in his grasp, screwed up and decided to mess around with Syria and Cilicia instead. His son Ioannes II was rather unfortunate in his choice of targets, as well, and had the wrong mind-set anyway. (Birkenmeier in his book on the army of the Komnenoi argues that Ioannes campaigned as a preclusive defense, not to attack, and in so doing kept the valuable provinces of the empire untouched while the Turks wasted their energies counterattacking useless forts. SO WHY THE HELL DIDN'T HE ATTACK TO GAIN TERRITORY? YOU HAVE ZERO STRATEGIC DEPTH AND VIABLE OPPORTUNITIES FOR EXPANSION AND PLAY THE PRECLUSIVE-DEFENSE GAME? IF YOU ARE DOWN BY FIVE WITH ONE MINUTE LEFT IN THE FOURTH QUARTER, AT FOURTH-AND-2 ON YOUR OWN THIRTY YARD LINE, YOU DON'T FRIGGIN PUNT, IDIOT! Okay, I'm done.)