First, let's discuss monopoly pricing. Given a competitive market, the optimum pricing will usually be not much higher than the expenses of production, because raising it will lose a lot of business. In a monopoly, the pricing is higher, but it's still limited. Raising prices will reduce the amount of business according to the demand curve, which is never completely inelastic. A monopoly, effectively, is an organization that can do monopoly pricing, not just one without competition. Microsoft Windows was and arguably is a monopoly, since there were no other generally acceptable desktop operating systems, so Microsoft could pretty much get what price it wanted.
A natural monopoly is a business where no competitor can effectively break the monopoly pricing. In the case of water companies, the cost of running piping to every building will normally be higher than the amount the competitor could earn by undercutting the monopoly, so we couldn't normally expect a competitor to emerge if there is a monopolist. (This is different from two competitors in a natural monopoly who each hope to be the monopolist.) Your example of different companies for different areas of a city is irrelevant, since the choice of water provider is completely tied to the location of the building. It's no different from having one water company for a city, and another for the next city over.
There's three reasons for such a natural monopoly that I can easily think of. One is that the infrastructure is very expensive, so the cost of duplication would be higher than the potential profit. One is that it uses an exclusive resource, such as limited space on utility poles or part of the EM spectrum. One is network effects, so the value of owning X rather than Y depends on the number of people using X and Y. Microsoft Windows is necessary for most people's computers because it reliably runs Windows-compatible software, and developers generally bring things out on Microsoft Windows because that's where the customer is. To compete effectively, an OS would have to reliably run Windows software, and there's lots of reasons that isn't going to happen any time soon. Consider what happened with early nettops, low-end laptops that ran some sort of Linux variant and were intended to run web software. They didn't sell because they couldn't run Windows-compatible software. It wasn't until Apple transformed the smartphone and tablet markets that there was a big market for OSes that weren't Windows.
There are also situations where there doesn't have to be a monopoly, but where one would be much more efficient. I've lived in a city with city-coordinated garbage service and one with hire-your-own, and the former worked a lot better. Trucks had to travel shorter distances for the same business, neighborhoods had uniform garbage days rather than having garbage trucks running around and messing up traffic at any time, and people didn't try to evade paying a garbage company by stuffing garbage into other people's bins or just dumping it somewhere inconspicuous.
So, we've seen ways to get natural monopolies, specifically through barriers of entry and network effects, without involving politics. The political reaction, in some of these cases, has been to grant a de jure as well as de facto monopoly on the condition that the monopoly is regulated. (This can happen in various ways. My water and sewer service are supplied by city government departments, my gas and electricity and phone service by regulated private companies, and my garbage collection by private companies that bid for city contracts. All work well at reasonable prices) The other political involvement is in allocating scarce resources. Somebody has to decide who can use what chunk of EM spectrum, and on what terms. Somebody has to provide easements on public and private property, or it would be completely impractical for anybody to build out infrastructure (some property owners would refuse to cooperate at any reasonable place).