what was the function of the Roman cavalry?

[Tarbicus]

I see your point, but I still think that the Triarii, although probably very shocked at the event, would still be able to repel cavalry from behind by simply turning about and the officers swapping places. However, morale both at the front and the rear would be crushed, inducing panic right throughout the Roman forces. One of the biggest problems would be that there could have been a rout at the front, but they had nowhere to go. This could leave disorganised gaps in the formation and smaller groups of units on the outer part of the army undefended in turn on their flanks. The Carthaginian forces could "eat away" at the edges more easily, especially with the use of slingers, which we know happened (any attempt by a unit to charge the slingers would expose their rear and completely cut them off). It mightn't even have taken actual close engagement by Hannibal's cavalry at the rear to cause a disastrous upset to the Roman formation.

It's also not likely that the Roman soldiers would know exactly how many had engaged them at the rear, given the immense area the battle covered. All it would take would be for a rumour to spread like wildfire through the ranks that they had been ambushed from behind by reinforcements, many of the men at the front and centre not even being aware that there were major cavalry engagements to the flanks and the Carthaginians at the rear were only those very cavalry.