It's nothing to do with blood, it's about society and politics. Rome itself would come to suffer a great deal from brutal civil wars, political fragmentation and weakening of centralized government.
I don't see how that would really change much of anything, at least not to the advantage of Rome. They would still need massive resources invested to keep such frontier pacified. With great distance and lack of communications the local gorvernors would find it all too easy to ignore Rome and set themselves up as petty kings. In return Rome wouldn't get much, especially from Germania where agriculture was very limited due to lack of necessary technology.
Anyway, logistical difficulties alone would make it extremely unlikely that either empire could refuse to "rest until the other had been completely destroyed". In such hypothetical situation they'd more likely exhaust themselves as in the last Romano-Persian war which set the table for the Islamic expansion out of Arabia...
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