what was the function of the Roman cavalry?

[Robert Vermaat]

Yes I agree. I have seen horses prepared to ride into infantry who are not armed with long weapons. One horse was out of control and easily split a formation. Another was ridden up to the infantry line, held in balance, then kicked on into the shield wall easily breaking it. But these are the exception, and the infantry were not trying to kill the horse!

Not trying to kill the horse and trying not to be injured themselves!
We did similar 'light training' (new to horse ánd shield wall), and we knew how to split before the horse went through us (below)!

I think that in a situation of battle, these horses would have had more trouble breaking up the formation.