When the free market doesn't provide

I read an argument recently that showers (and other water-consuming devices) shouldn't be flow-constrained through legislation, and that water should just be priced much higher.

Here's the problem with that: water, while a renewable resource, is at any time limited (unless someone invents cost-effective desalinization).

So say there's 350 gallons of water available every morning for... five families, with four people in each.
1 makes $20k
1 makes $30k
1 makes $40k
1 makes $60k
1 makes $100k

That's not far off the actual income distribution in the US, even though I'm fudging a little for the sake of this example.

Each house uses about 65 gallons of water a day if they're using low-flow showerheads, toilets, and everything else. That leaves about 30/gallons a day in this random example, but everyone's needs are met, and while the fixed cost of water hits the poorest home the hardest, it's not as if they can't afford to drink.

So let's say you allow houses to use as much water as they want, and throttle demand based on the market. Set the initial cost at $1/gallon. Out of the gate:

$20k uses 65g, pays $65
$30k uses 65g, pays $65
$40k uses 65g, pays $65
$60k uses 65g, pays $65
$100k uses 65g, pays $65

With 30g left over. The richest house gets super high-flow showerheads and starts taking longer, luxurious showers, because heck, they can afford it, and who doesn't love a good shower?

$100k uses 90g, pays $90

The surplus has already gone entirely. The $60k house then decides they'd love to have equally luxurious showers... except now we're in trouble: we have to hike the prices on water to get another 15g in the system. The 100k house is almost immune to price hikes, of course... and it's the 20k house that gets really beat up when you double the price:

$20k uses 55g, pays $130
$30k uses 60g, pays $130
$40k uses 65g, pays $130
$60k uses 90g, pays $180
$100k uses 90g, pays $180

And so on. The increase in water price hurts the poorest household 5x as much as it does the rich one. They're jumping in and out of the shower, skipping days, and generally being smelly and miserable... because at the high end, the resource they need is being used for luxury items.

I know at some level that this is the way of the world. But it seems clear that when dealing with a limited resource that everyone needs to live, universal consumption restrictions are just and beneficial to the whole.