Why would that stop the RCC from using the invention of the printing press to widely distribute Scripture to it's congregants?
You know, I hope, that we didn't spring directly from hand-copied Bibles to paperbacks produced by the millions for 25 cents a copy?
The early printing presses printed one side of one page at a time. You inked them by hand. You might make 3 pages a minute, if you were good.
Nevertheless, by the time the Reformation started in England, it was common for reasonably well-off people to have a printed "primer," which was a combination catechism, missal, and often contained portions of Scripture, especially the Psalms or the Gospels. Some of them were in English and some were in Latin, but almost everyone who had been to school could read Latin. Those who hadn't been to school couldn't read, period.
You need widespread literacy first. That probably took a couple generations. As an analogy,
Before the Gutenberg press, and the associated increase of literacy, those who needed to know how to read knew how to read Latin. There was no grand conspiracy to suppress the vernacular Bible; just cold, hard economics. Even so, there were English translations by Alfred the Great (ca. 900 A.D.) and the Venerable Bede (ca. 735). for catechizing use; Charlemagne had a translation of the Vulgate made into Old High German around 800 A.D.
The Church's objections to the new vernacular translations were not that they were made, but that they were misleading in the Church's opinion.
This whole Catholic conspiracy to suppress the Bible is the product of the imagination of propagandists, not history. Unfortunately, it is indelibly ingrained in the Protestant subconscious.
>> Why would that stop the RCC from using the invention of the printing press to widely distribute Scripture to it's congregants? <<
It didn't. The illiteracy which persisted because of the newness of the press did. Those who were literate could read Latin. The Catholic Douay-Rheims bible (1582) preceded the Saint James Bible (1611), for instance, but relied heavily on Latin terms, because adequate translation into (then-primitive) English was impossible.
One thing about the King James folks is that they are so used to given bible phrases being understood in one way, they often fail to recognize the ambiguity created by the fact that, at that time, English was largely useless for developing complex arguments.