The famous Roman sewers carried away very little human urine because the Romans saved it for various uses. If you added pee to your laundry, the ammonia in it served to keep whites white, so it stands to reason they would have believed it would do the same for your teeth.
And it was a key ingredient in dying (very expensive) indigo cloth. Businessmen sometimes built toilets for public use, hoping tho recoup their investment by selling the urine they collected to the dying industry.
The Emperor Vespasian even taxed the business of collecting urine from public toilets, which goes to show you that even 2000 years ago, the government couldn’t resist taxing any business that turned a profit.
Urine was used by fullers to process wool, and the public urinals were provided by the state, so, yeah, taxes. One of Vespasian's sons (both of them eventually succeeded him) complained about taxing urine, so V gave him a coin and told him to smell it. He smelled nothing. "That's odd -- it comes straight from the urinal."