Depiction of ship mills under a bridge in Paris, France, ~1317 AD

Thanks! I thought so, but kept wondering “why?”

Turns out, according to Wikipedia:

Floating allows the mill to operate with the same power despite changing water levels.

It was invented at the tail end of the Roman Empire, 537, to continue flour production during a siege of Rome. So it looks like the biggest pull was the flexibility of location.

When waterways became more congested with traffic, they became a hindrance and usage declined.