Cleaning up water takes a bit of energy and so does heating it up. So yes, it has a price. However, we know how get clean energy now. So, that's a solvable problem. And it's not that expensive even. High gas prices are currently causing people to think very hard about how to upgrade their houses. The real money savings are house heating. My parents switched off their gas heating system a few weeks ago after being faced with 1000 euro monthly gas bills. Only a fraction of that is showers. It's a recently renovated house that is pretty well insulated. The issue is simply that gas is really expensive now. Luckily, they have a wood pallet stove. Also not cheap to run but a lot cheaper. The real solution for them will be a heat pump and some access to renewable power. And the financial incentives for that are there now in the form of high gas prices.
I agree. But I'd add that the idea of a mist shower is great if you are doing something off-grid or boondocking in a camper, where every gallon counts.
While I understand their concerns around energy usage, the focus and on water usage (or implied "wastage") feels, to me who lives in a very different country, rather odd.
That water isn't destroyed, it'll be back eventually, assuming we're not consuming fossil water.
It's definitely good to reduce excessive water usage, just from an infrastructure and sustainable water take POV, but this reminds me of the concerted media effort around climate change to make it the individual consumer's responsibility to reduce emissions, taking the focus away from the corporations whose profit has always come with an atmospheric externality...
In other words, if you want to save water in Die Niederlande, look at industrial/agricultural usage first, showers third, after "let's maintain pipes to minimise leaks".