I see what you are saying, but this only looks at mining or trapping luxuries. You cannot connect quarries or plantations by turn 10.
It also assumes you meet an AI who has 6-8 GPT to trade, which means 8 or 10 gold total because they don't trade the last 2 gold they have. I just had this situation play out, Zulu values my luxury at 7 GPT, but has only ever had 5 positive GPT in the ancient era. My other neighbor, Carthage, only values it at 3 GPT.
I realize that this is a very good start when it works, and you should give up a bath in that situation. But that's really specific, and you have no way of knowing how much gold AI you meet will be able to trade. The tile also won't qualify for pantheons, granted isn't that big of a deal for mines or camps. Even among mines, a salt hill is a crap tile to put a city on, I would much rather have a mine there when building settlers. You also won't get bonuses like forges to the tiles, because it's not a mine, it's a city.
If you are talking tradition, you really want to hit 4 pop before you take your social policy. That means that 3 food for flat freshwater is really important. Taking tradition at 3 pop gives you 105 food (43 + 62). At 4 pop you get 146, a difference of 31 food.
Baths have a base of 2 culture, get another 2 if you have tradition, and have a synergy with gardens and amphitheaters for another 3 culture and 3 gold. That's an extra 7 culture without golden ages.
I actually think I'm most likely to do this with Marble, because you can get the 15% towards wonders instantly and use it on Stonehenge or Pyramids. Or a faster monopoly, like settle on tobacco to get the faith monopoly sooner, plus then you don't have to work a crap tobacco plantation.
TL:dr
It's sometimes right to give up fresh water this way, but not always.