As far as I can tell, here's how the justification that it's a crime worth charging goes:
1. Would Stormy Daniels announcing weeks before the election that she and Donald Trump had an affair have impacted the election? Yes.
2. Was the (perfectly legal) money paid to Stormy Daniels to prevent that thus intending to influence the election? Yes. Ergo, it's a campaign expense.
And here's where it turns into what I believe they'll be charging.
3. Knowing the above, did Trump funnel the payment through Michael Cohen with the intent to conceal it from campaign finance disclosure transparency? If so, that's conspiracy and a felony through falsifying business records to conceal another crime.
If you break the law inadvertently, that's generally a lesser crime. If you specifically know you're breaking the law and still do it, that's usually a higher charge. And if you take additional actions to conceal the fact that you broke the law, that's an even higher charge.
And because these are financial crimes, it's easier to find records of the intermediate payments.