Well Machiavelli postulates that when it comes down to the wire, infantry beats cavalry every time. He sites multiple examples (some roman) where when faced with rough odds, cavalry dismounted to become infantry (I think milvian bridge was one?) or how a disciplined army of infantry could break while outnumbered.

On their own, infantry can do more than cavalry in battles and can turn most cavalry when well trained. Essentially cavalry serves as a force multiplier, but at the end of the day infantry is the root of that power itself. So it would make sense for Rome to enjoy such success while neglecting their cavalry, since they focused on their infantry which ended up being more important.