sasanid empire was ill and engaged in multiple fronts against different enemies. they were fighting each other over throne, eastern Christianity was infiltrating into Iranian society and Zoroastrian priests were not happy of it. feudalism and the atrocities of royals on peasants caused a fracture in society. the royals were too cocky and couldn't see beyond their noses. byzantine empire were invading their western borders, gokturks were invading the northern borders and non Muslim Arabs were raiding their lands from south and finally Muslim Arabs that put an end to them.
mobility had it's own advantages, US scouts invading Iraq used buggy cars to bypass defending troops and neutralize enemy air defenses and commanding centers and prepare the begging of invasion. it gave them the advantage of riding through desert and avoid enemy but if they were not fortunate enough and an emp-2 were in their pass they would have been decimated.
the same goes for the ancient era, however cataphracts were mostly engaging feet soldiers not cavalry.
i'm not an expert or anything but i guess the the reason Turks or mongols were so successful is their way of managing the logistic part. if i'm not wrong the bastirma is a Turkish food which originated from the tribal living era. Turks also were always riding and even eat while riding it makes them super fast. also i read some story about tanto(?) horses that were capable of travelling twice the ordinary horses.
after sasanids ME countries did not had any heavy cavalry units beside a failed attempt of Fatimids to copy crusaders knights which they couldn't live enough to deliver it. and unfortunately it had a bad effect on the course of crusades.
