Explanation: The Roman military was one of the most refined and powerful of the Classical era.

... it also never really developed a strong native tradition of cavalry, despite cavalry being one of the two very basic and necessary arms of pre-modern warfare.

The Romans, you see, believed that all peoples had special skills. The Romans believed that their own special skill was not art, or science, or even fighting - but organizing and governance. They believed that their ability to judge and put and use people in the right places was what brought them victory (and, conveniently, made them uniquely suited and deserving of ruling over 'barbarians' - purely coincidentally! It's for their own good, don't worry).

The Roman way of life, as predominantly oriented towards farming and urban life, did not particularly privilege or encourage lifelong traditions of ridership, so the Romans were always aware that their own native cavalry was... at best, middling. As such, Gallic (France), Spanish, Germanic, African, Arabian, and Scythian (Eurasian Steppe) cavalry were all preferred (in different specialties) over native Italian riders!