what was the function of the Roman cavalry?

[Tarbicus]

ie an attack from the unshielded flank and rear....?

It's not likely that the infantry would allow themselves to be charged without turning to face the cavalry. Even at Cannae, where exactly that happened, the Romans were bound to have turned and faced the Carthaginians. However, making the reserves do so would probably obliterate morale in the forward ranks, as they would have nowhere and no backup to retreat to should the need arise, which du Picq emphasises was a stringent necessity for Roman armies.