An anecdote only: I won’t try to turn it into a thesis since it’s merely an observation.
The habit of using the Law of Moses as a way of filling in any perceived blanks left by the writers of the New Testament seems well ingrained among the supersessionist Reformers I encounter. For example, there are many discussions online about tithing these days. These almost inevitably take on a quasi-legalistic tone (“What must I do?”).
When you think about it, this makes some sort of sense.