Here in WaPo, amusingly turning the matter back on Mueller at the end:
However, regardless of what Cohen agreed to in a plea bargain, hush-money payments to mistresses are not really campaign expenditures. It is true that “contribution” and “expenditure” are defined in the Federal Election Campaign Act as anything “for the purpose of influencing any election,” and it may have been intended and hoped that paying hush money would serve that end. The problem is that almost anything a candidate does can be interpreted as intended to “influence an election,” from buying a good watch to make sure he gets to places on time, to getting a massage so that he feels fit for the campaign trail, to buying a new suit so that he looks good on a debate stage. Yet having campaign donors pay for personal luxuries — such as expensive watches, massages and Brooks Brothers suits — seems more like bribery than funding campaign speech.
That’s why another part of the statute defines “personal use” as any expenditure “used to fulfill any commitment, obligation, or expense of a person that would exist irrespective of the candidate’s election campaign.” These may not be paid with campaign funds, even though the candidate might benefit from the expenditure. Not every expense that might benefit a candidate is an obligation that exists solely because the person is a candidate. ...
Cohen is not the normal defendant, and prosecutors almost certainly squeezed him to plead guilty on these charges, in part, for the purpose of building a case for possible criminal or impeachment charges against the president, or even, daresay, “influencing the reelection” of Trump.