They didn't need to. The Roman and Persian wars were not one-sided defeats. People only think of Crassus and Anthony's defeats yet forget or are unaware of the major victories won by Trajan, Severus, and Galerius.

Trajan conquered what is now Iraq from the Parthians and incorporated into the new province of Mesopotamia (which his successor Hadrian abandoned as he felt it couldn't be defended). Both Severus and Galerius successfully waged wars against the Parthians and captured or sacked the Parthian capital of Ctesiphon. Galerius' victories were so destabilizing to the Parthians that it triggered an internal revolt that toppled them and replaced with with the Sassanid Empire.

The battle of Carrhae seems to be fixed in people's minds and the victory of horse archers over the legion. Yet that's not quite what happened. The Roman army spent the day getting shot at and undoubtedly took many casualties but when night fell it was still an operational army capable of fighting. What turned it into a catastrophe rather than just a shameful defeat was Crassus losing heart. His son had lead a cavalry charge that tried to get to grips with the Parthian archers but had been drawn away from the Roman army and destroyed by Parthian cataphracts that were backing up the light cavalry. On the following day, Crassus went to negotiate with the Parthians and was treacherously killed. The somewhat rudderless Roman army then attempted to retreat but was destroyed in the process. So it's more than just horse archers turning legionaries into pin cushions. It was successful because it was backed up by cataphracts and against a force lacking sufficient cavalry - because the Armenians Crassus expected to bolster his forces never arrived.

As we can see from Trajan, he took a similar army (albeit more professional) and achieved a resounding success. The Roman military system was clearly not inferior.