Sorry, no that was most definitely not how Christianity spread, at least for the first 300 years after Christ. You refer to the Dark Ages after Constantine paganized Christianity and declared Rome to be its center.
The Roman Catholics were Bible-burners. Private ownership of the Bible was forbidden. The Bible was in Latin, interpreted by priests.
The Protestant movement was essentially departure of Bible-believing Christians from the Catholic Church, and the end of the Dark Ages. In effect, anyone could read it.
And in modern times, we have free digital copies of the Bible, effectively fulfilling Daniel 12:4:
But thou, O Daniel, shut up the words, and seal the book, even to the time of the end: many shall run to and fro, and knowledge shall be increased.
If you think we cannot go back to Fahrenheit 451 style book-burning, I think you are mistaken. The censors are essentially book-burners. And that should trouble any liberty-minded person greatly.