@LSCatilina If I read you right, you're saying it is impossible because the Romans were unable to influence the other Christian countries in the same way as before?
It goes deeper than this : not only Romans were wasting large ammount of fiscal and strategical resources in their wars against Sassanids, but they were unable to use nearly as much they could before, outside the empire proper, but as well in Italy, Africa and Balkans.
It's not enough to conquer regions : there's the problem of maintaining a control over these with more limited fiscal resources (which were already made more vulnerable by Justinian's policies, giving that you couldn't really count on Africa and even more Italy to supply itself entierly).
Lombards up to the last Romano-Persian war did enjoyed a particularily favourable situation, as the Gothic War (due to poor political and strategical assumptions, IMO) was particularly disruptive. But up to the 570's, they remained fairly stuck in the north of Annonarian Italy, and anything south of Po where you had a Lombard presence was possibly not really controlled before the end of the Lombard Interregnum.
Not that the vice-royaltisation in Italy or Africa wasn't a sound idea : I think that Mauricius western policies were mostly spot on or at least coherent. But it was made at the cost of some neglect (Africa is barely mentioned in imperial chancery at this point, for exemple; and Roman Italy became sort of vice-royal confederation of Duchies) and for being less costly for the empire overall, it still required some exchanges dominated by Constantinople in provinces that were either "other Christian countries" but as well the vice-royalties that Exarchates were.
I wouldn't dismiss the importance of the role of the Empire for Trans-Danubian chiefdoms, tough. The presence of a strong empire and the its capacity to influence and balance entities as Lombards, Gepids, Kurtigurs, etc. was critical to the stabilization of the border, would it be to avoid the emergence of a complex or super-complex chiefdom, and to advance that a peaceful relationship with the Empire would be more awarding than warring against it. With the emergence of Avars, the lack of strategical resources to fend off these as it was the case with Kurtigurs, and a lesser capacity from Constantinople to sustain a court/emporia relationship with trans-danubian entities...
None of this happened overnight, of course, but the combination of the lack of military and strategical ressources and the unability to project itself trough a controlled trade or gift exchanges was certainly a main reason for the Empire to be unable to maintain a certain rule in Italy and Balkans (Africa is another case, mostly because of the absence of Saharian threat, even if eastern Berber chiefdoms did collapsed or submitted quickly, opening Tunisia for Arabs).
Whilst the expounding on the Byzantine method of influence is certainly interesting, I'm not sure it answers the question. (Either that or my mind is thick as mollasses today).
I tried to precise my point just above in a manner that may satisfy you, altough I agree there is a component that I didn't mentioned, while it was related to the weakening of imperial role and authority, namely the religious opposition.
Imperial religious policies such as monoenergism and critically monothelism alienated them a lot of support and credibility in the West (possibly more in the western provinces and exarchates than within Barbarian kingdoms). It tends to be dismissed on this board because...reasons I guess, but in conjunction with the growing independence of these region and the support Roman pontiffs knew they could count on, did its job to prevent a certain imperial loyalism to appear against its withdrawal.
As in, the Arabs don't manage to counter Greek Fire
They didn't. A good part of Roman survival comes from that Arabs never really managed to break the supply chain in Mediterranean basin.
don't build fleets large enough to oppose them or a prevented from doing so
Early Arabic seafare was mostly due to the relative inclusiveness of the Arabo-Islamic entities : where existed a strong naval tradition, it was maintained and developed. But it wasn't from scratch : the famous
Battle of the Mastes involved an essentially Coptic and Syrian-issued navy rather than Arabic.
It doesn't mean that Abul A'wal was clueless on seafare, of course, and his previous raids in eastern Mediterranean proove that caliphates could perfectly well use naval warfare.
A good part of Byzantine-Arab naval conflicts was more a game of cat and mouse up to the late IXth, searching to avoid big clashes unless a clear advantage was obtained (and Romans did changed their strategy first because they had so, tactically and qualitatively), and the Battle of the Mastes is one of the exceptions, possibly due to sheer incompetence of the basileus, who didn't ordered any fighting formation.