Isn't the property tax most places based upon the value of the home? So adding a pool will increase the value of the home. Normally though there's a tax assessor that goes around and should be looking at every lot and assign a new assessed value, though in practice I think they just google if the prices in the neighborhood have gone up or down.
A lot of government in the US works by assuming most people are generally lawful, and they're not going to just start adding rooms onto the house without filing the paperwork first. For taxes they do some random audits on a small subset. This generally works, those breaking the rules aren't too many and don't get away with it for too long (often neighbors turn them in, they get very nosy when construction starts). But this all breaks down if you have wholesale cheating going on, such as Greeks with taxes awhile back, and perhaps these Argentinean neighborhoods.