Water supply is never an issue, all that's treated is adding chlorine.
This is so wrong.
Water resources themselves are finite to a degree, because the current infrastructure is more focussed on upland rivers and groundwater sources. The recovery time on these stores can be naturally long and are being effected by lower rainfall than historical averages. Also, the Environment Agency are getting harder on sustainable abstraction, restricting take from more sensitive sources to protect habitats.
Water could be replaced from lowland rivers, even the sea, but it is more costly to treat. You are also wrong that 'just chlorine' is added lol. Treatment processes use a wide range of physical and chemical treatments which are expensive. Removal of particulates with various types of filtration, removal of nitrates with ion exchange, removal of pesticides with granular carbon plus many more. All these cost money.
You also dont pay for as much as you like, you might think you do, because you can, but you dont.
Water companies use demographics to estimate the consumption levels across their customer base, which in turn feeds into tariff setting. You are actually paying for average use. If you use more and someone else less, then they are cross subsidising you. I totally agree this also applies to the NHS, but let me put it this way- would you expect an old lady using hardly any water herself to subsidise your garden watering? What about your energy use as well then? How about she shares the cost of fueling your car too? Its in this context that metering is the fairest way.