I didn't explain it well. Not pagan government alone who tried to rule the world from Babylon, to Medes, Persia, Greece, to Roman Empire, but the fear that that would arise out from within the temple of God (the church, the body of Christ). The idea was that the Roman Empire "held back" the man of sin, the one who exalts himself. Chrysostom and Tertullian and others for example prayed the Empire would remain. Caesar was god, worship him if you're not a believer, but he's outside Christianity. So when the Empire fell, the vacuum opened for another system already in place to take over.
So, the comment was there was a fear that Christianity would fail if Rome fell, but that isn't necessarily the whole story. The church fathers prayed Rome/Caesar would remain to withhold (hold back) the man of sin. Christianity was subject to the government. Paul said pray for the rulers. Those fathers feared, however, that what was outside would come inside (already at work Paul said) as the man of sin (son of perdition) grew into power to rule kings and others. Take over the world. It wasn't Caesar who would be the problem.