Firstly it's not structurally practical to store giant tanks of water on private property. So the comparison makes no practical sense anyway.

But more, there is a significant market for private water in other properties. It's a non-trivial market which serves a significant proportion of the US population.

There is no significant market for private/non-Google search. Not only is DDG a footnote, but Google's dominance forces businesses to take steps to optimise their Google rank - or face penalties by losing access to potential customers.

Google can also remove businesses who aren't even customers from its rankings on a whim, with no redress.

It's clearly a monopoly.