Oh, I am sure that some churches did not have all the NT books for some time.
But I disagree that it would have taken a hundred years or more for all the books to get around to the churches. Yes, travel and communication were much slower back then, but they did an amazing job of getting around quickly. They had couriers, they had ships.
But you know what, this is all speculation on your part and mine. There is no way to go back in time and know exactly which churches had which texts. And I am sure it might have changed at times, one church may have loaned a text to another for a period of time.
So, your arguments are just as speculative as mine. You do not have any proof of your assertions any better than I do.