Since most people take the New Testament completely out of context, anyway, that wouldn’t be a bad idea. Even the Catholic church, which does the context / gospel sandwich in liturgies, doesn’t use the whole old testament. They could just keep the parts that are necessary for understanding.
In my opinion, the old testament isn’t nearly as bad as the reductio ad absurdum arguments in the new testament. Assert a premise. Develop the logical conclusions of that premise. Determine that the conclusion is contrary to your intention. Therefore, the premise is invalid. (And annoyingly, many times it was assumed that you’d REALIZE that, so it is never explicitly stated.)
Unfortunately, too many people read the assertion in the Bible and say, “The Bible says…” They don’t consider the whole argument, or get to the part that refutes is.
This used to drive my theology teacher in high school up the proverbial tree. (He was the same one who said a favorite game in seminary was for someone to give a bible passage, and someone else had to call out a passage that contradicted or refuted it.)