I've never cared for the "if it doesn't appear in the novels, it shouldn't appear in a game" approach. Not sure if you mean it to that extreme, but I've seen that so many times over the years. Some people don't even add towns or villages to their maps for Middle-earth games if they weren't specifically mentioned in the novels. While I guess that's respectable purism, it's purism to the point of dullness, because to me the novels covered a very specific set of characters in very specific areas on a very specific path to a very specific place. There's worldbuilding in there, but almost everything with any detail is what's immediately important to the characters and the stories. To strictly adhere to that approach where Tolkien intentionally left out large amounts of world detail doesn't translate well to a game, where the story's important but you want it set in an interesting world, which you need more detail for and will inevitably have to take creative liberties with.Crossbows feel out of place because: 1) they don't appear in the novels; and, 2) they are generally thought of as innovations of the late Medieval Period (few people realize how far back they really go). Also, Tolkien tended to shy away from that degree of technical innovation in the legendarium.
As for the "late innovations" idea, yeah, I'd say in general people probably think crossbows just picked up use shortly before guns did, but obviously they go back further. It's interesting to bring up how Tolkien would feel though, since apparently one of the earliest depictions of a crossbow in Northwestern Europe was found on Pictish stones in Scotland dated to as far back as the 400s, so well before the time period Tolkien would've intended to vaguely represent and in his general region/culture of choice for his stories' inspirations.