a semi-informed guess is that paper checks are uniquely useful for entering some kinds of contracts between ordinary people or small business. A check here has only five or so parts, but by controlling those well, checks can and are used in somewhat unexpected ways, and they can be formed to fit various ordinary contract clauses, too.

one surprising use of a check is that one could write five checks, each with an amount and further away date.. e.g. dated the first of the month for the next four months. Those checks are now a reliable source for a loan in cash, since you signed each one. there are many other examples..