Additionally, the worst strains on the grid are really measured by the peak loads, so if you change billing a way that makes the peak energy less expensive, and therefore disincentivize people to (a) reduce usage at peak times or (b) install solar panels/batteries to mitigate their peak usage, then it actually might make the grid more unreliable.

Water is different in that we really only have usage concerns about water, AFAIK there is never any issue with the water pressure drops at peak times (perhaps thanks to water towers). With electricity the concerns are mostly about the peak usage, and not so much the overall usage.