>>Romans were the first to flush toilets

To be fair, they didn't 'flush' in the sense that we think of; instead, there was a constant flow of water. The Romans didn't have water valves, houses paid for their water supply based on the diameter of the inlet pipe. And I've seen some mention that Crete, at the height of Mycenean civilization had something similar in the palaces (but not general use).

As far as public health, I'd expect lower levels of intestinal infections (e.g. cholera, polio) coming from drinking water brought in via aqueduct rather than sourced where there might be contamination from sewage. Rome might have been a public health high point until the mid 1800s with the advent of "sanitation committees" during the American Civil War.

All that said, the tersorium makes me think of a Amazon product review for a toilet brush. Paraphrased, it went "much too rough, going back to toilet paper - returned it". IMO, there are gems of hilarity mixed in with those reviews.