First, your napkin math is shit. They aren’t carrying 6000 pounds of water for the 14 first class seats to get 5 minute showers.
Second, the water they use per person weighs less than the weight of the extra passengers that could be fitted in if the arrangement wasn’t first class cabins but was instead economy. First class passengers are where all of the margin is.
Finally, you don’t seem to understand what “market efficiency” means because it has nothing to do with this.
You're right https://aviation.stackexchange.com/questions/11132/how-much-... it's much less (350 KG). Elsewhere they do say the showers are marble and mirror. So extra weight. I assumed without checking there would be lots of first class passengers, got it wrong.
> you don’t seem to understand what “market efficiency” means
If the fossil fuels were costed appropriately, there'd likely be no flying, certainly nothing like this. So its mispriced, is what I mean.