If someone had an idea that they wanted to spread, and they knew that it would likely reach a broader audience, have more sway, and last longer in history if they were able to pass it off as someone else's words, wouldn't that be a reasonable thing to do?

Certainly, not everyone would try to do that. But if lots of scribes make lots of hand-copied text over the years, it seems reasonable to me that sometimes people would slip in ideas of their own.

And indeed, we see that all the time with historical texts - not just the Bible. So this just seems like a silly argument to me.