Cooking, refrigeration and water pumping depends on electric power. It can definitely get nasty if it lasts for more than a day
This is exactly it. The other part is not just water pumping but operating the sewer systems - if the lift stations are down the whole thing fills up in about a week and the basic plumbing in your house - and thus pretty much entire city, stops working.
Cities are not setup to support their current populations without those services and once you run out of buffer things go downhill quick - wastewater is an enormous and immediate disease hazard.
This is one of the reasons I'm looking at extending my solar system to add a battery and islanding, so I can have a regular resupply of some amount of power/electricity for the necessities in case of extended outages.
I'm not sure how far into "prepper" that makes me. I don't have a store of canned food or weapons or a generator. I started down this track to keep my home lab (on which I self-host a bunch of stuff) online / protected through outages.
Additionally, the city in which I live has an ad-hoc amateur WiFi setup which connects over several kilometres. I used to be a member a long time ago but, ironically (in this context) getting fiber internet meant I kinda lost interest. It's one of those things that had just never gotten back to the top of my priority list: https://air-stream.org/
Feels like they're ahead of game on this topic.