You can't just stop supplying water to distribution pipes: that would create widespread pressure drops and consequently huge areas would be entering boil water advisory situations, and testing water after a mains pressure loss gets expensive.

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Electricity is a (mostly) national grid while water systems are closed off systems serving much more local system.

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Likely because the infrastructure isn't set up for it. But also because potable water systems have more issues than an electrical grid that would exacerbate the issue.

Firstly, water supply is generally a much more gradual process. Sure there are demand peaks and troughs, but it's not as reliant on immediately supplying the quantity consumed in the same way as electrical power is. Where there are high demand spikes, passive buffer systems like water towers naturally smooth out the demand. The supply issues are generally on the scale of weeks/months rather than minutes/hours.

Secondly, you can't just shut off a potable water system for a bit. When a supply is shut off, inevitably the downstream system loses pressure. This is a problem as you can never guarantee there are no leaks - there are often dozens of active leaks at any time, but small enough to have a limited impact and not be worth repairing in the short term.
In normal circumstances a leak isn't a huge deal - sure you lose a bit of water, but that outward flow with the pressurised water pipe keeps contaminants out of the potable supply. When the water is shut off, dirt, debris and microorganisms can instead enter the pipework, particularly with buried pipes (like much of public distribution pipework). As a result, the system isn't safe for drinking water until the contamination has been flushed out - usually a couple of days to be sure, which may or may not involve additional chemical dosing. During that period, the water company has to instruct everyone connected to that system not to drink the water/boil it and/or supply alternatives (usually bottled).

ELI3: turning water off makes pipes dirty. Turning electricity off just annoys people.

You mean... cut off peoples' water? The thing you absolutely need to, you know. Survive?