Let us assume for the sake of argument that all of what these things were absolutely true (although its doubtful they are):
Trump still was not guilty of even second degree falsification of books. The payments to Cohen were indeed legal expenses and thus the entries were factually true. Nor was anybody defrauded by the entries, since the election was over when the entries were made.
Should one care to argue he should have entered as "reimbursing black mail payment" as being more precise than "legal fees" then by that absurd standard Alvin Bragg's charges are breaking the same law since they do not reveal his motivation to interfere in the current election.
If I understand the argument Bragg is claiming it should have been listed as a campaign expense. Which is illegal. You can not even buy a suit and put as campaign expense.