WI: Barbarian Kingdoms Survive (No Byzantines)?

Hello all. I'm a long time reader, first time poster, so I thought I would posit an era of history that isn't that often considered in Alternate History discussion: Post-Fall of Rome but Pre-Byzantine Reconquest.

Assuming the Byzantine Empire is prematurely weakened - say, Justinian I is deposed during the Nika riots - and doesn't try to reclaim the west, would the barbarian kingdoms (such as that of the Vandals, Ostrogoths, and Burgundians) have survived, or were they doomed to collapse sooner rather than later?
 
Burgundians were conquered in time by the Franks in OTL, and even with a respite from Byzantium, the Franks were tough fighters and simply wouldn't give up. Burgundy'd be conquered eventually. Same for Vandalia vs the Arabs.

Ostrogothia is interesting, because it could mean a unified, continuing-to-exist Kingdom of Italy. Even if it DOES split up via feudalism, the CONCEPT of a united Italian kingdom would be much more existent vs OTL. It would also be far more prosperous without the horrors of the Byzantine War inflicted upon the peninsula.
 
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