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.