You're broadly right, but they were popular for most of the period we're discussing.
In continental Europe they were popular from roughly ~1000 onwards (see Behre 1999), in England from roughly 1500 onwards. In African and South American farmhouse brewing they're still not used. So it's a pretty complicated picture.
As the comment made clear, hops are only one component of what makes beer safe, though. Storable, safe beer for travel is documented already in Ancient Egypt.
In continental Europe they were popular from roughly ~1000 onwards (see Behre 1999), in England from roughly 1500 onwards. In African and South American farmhouse brewing they're still not used. So it's a pretty complicated picture.
As the comment made clear, hops are only one component of what makes beer safe, though. Storable, safe beer for travel is documented already in Ancient Egypt.