The difficulty here, as I understand it, is that Trump could have plenty of reasons for paying off someone, not all of which are to do with political campaigning. For instance, he could argue that he paid off SD to avoid damage to his relationship with his wife or family, and that it had nothing to do with his campaigning.
(In fact, you could argue that this defence is even stronger because he is Donald Trump. He has plenty of dedicated supporters who seem to stick with him regardless of his transgressions; accusations of infidelity might be less damaging to him politically than to other politicians!)
So, the prosecutors have to somehow convince a court what his intent really was, i.e. it's less about what he did and more about why he did it.
(In fact, you could argue that this defence is even stronger because he is Donald Trump. He has plenty of dedicated supporters who seem to stick with him regardless of his transgressions; accusations of infidelity might be less damaging to him politically than to other politicians!)
So, the prosecutors have to somehow convince a court what his intent really was, i.e. it's less about what he did and more about why he did it.