Most people don't have the equivalent of home internet plumbing in general. They have a hole drilled into the wall (by the ISP) where the all-in-one modem-router-switch-wap sits on a shelf. There's probably a third party service to get ethernet run through your walls, and maybe even replace your all-in-one box with something good, but most people are just doing the equivalent of getting water straight out of the water company's tap with no plumbing.
This, and also, it's much more common for internet problems to be caused by upstream issues not in the house (partly because of the situation you describe....not much to go wrong on the users end). It's very rare that a plumbing problem is because the main water line lost pressure.
Back when I still had ISPs that provided the modem + router, every single issue I think I ever had fell into one of two categories: a modem and/or router power cycle fixed it, or it was a broader network issue that had nothing to do with me or my particular internet situation (this is omitting the most common third issue: terrible customer service problems, but that's a separate thing)
Nice analogy!