I think people seriously are overestimating how weakened Persia was at the end of the latest round of Roman-Sassanian wars. Obviously things didn't go particularly well historically, but the arrival of Islam was an exceptional moment in world history in many ways. Sassanian victories had seen many Byzantine provinces lost and those provinces were ones that traditionally were somewhat restive anyhow. The Sassanian monarchy under Khosrau Parvez was, I think, on the cusp of a sort of political revolution and I think this trend would persist even after his overthrow and defeat. Both sides were capable of fielding significant armies even after the war - and thus I don't buy into the argument that either side was "weakened" to the point of being crippled. I think both states were reaching the bottom of their manpower reserves, but such things would, after a generation or so, come back into balance. The Byzantine peace in 628 was one of exhaustion not true victory.
I think a significant mistake though, is to assume that the Byzantine - Persian stalemate would continue indefinitely. Such moments of stasis generally don't last in world history. Imagining Roman or Sassanian dominance is equally unthinkable. Through it's entire history, even at its height, Rome never showed the interest or capacity to take and hold the Iranian plateau. Few westward conquerors ever did. Similarly, I doubt an Iranian-based state had the capacity to reconquer the Eastern Mediterranean. I don't think, post Seleukids, that such a thing is particularly plausible in the long run. That said, something, sooner or later, will throw off the balance.
I think, with Late Antiquity or the early "dark ages" it's easy to say what won't happen. Hard to say what would. I think that's what makes this such a fertile group for althistory, especially when you're willing to not treat the remnants of Rome as something sacrosanct but as a state among others.